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PRESTON

TERMINAL

UNIVERSITY
Student Name:

Course Code:
Course Title:
Program:
Semester:

EXAMINATION

Islamabad — K o h a t - Peshawar - Lahore
R e g . fmr
i

QM 4354
Business Statistics
MBA/MS
Summer 2011

PRE:S .''ON
UNIVERSITY
-LIBRARY

This is a t h r e e - h o u r examination and consists of review questions and p r o b l e m s .
You may a t t e m p t not m o r e than a total o f t e n review questions and p r o b l e m s .
Q. I a) Write and explain briefly the fields of Singular Statistics,
b) Define any FOUR of the following with examples:
i. Error
ii. Class-width
iii. Frequency distribution table
v. Class-limits

iv. Simple Random Sample

Q.2 a) Define with examples; i. Median
ii. Mode
iii. Variance
b) Differentiate between Mutually and Non-Mutually exclusive events with examples.
Q.3 a) Assuming the following approximate numbers are correctly written, how many significant digits
does each have? (a) 21.80; (b) 0.0162; (c) 0.085 billion; (d) 4.00; (e) 1002.3; (f) 0.005.
b) Round the following to three significant digits: i. 307.42
ii. 0.046874
iii. 128,502.81
iv. 3.055
v. 21.3172
Q.4

From the following table compute;

Q.6

Q.7

ii. 1QR

iii.

/

Weight
6 5 - 84
85-104
105-124
125-144
145-164
165-184
185 - 2 0 4
Q.5

i, Coefficient of variance

9
10
17
10
5
4
5

Using the table of Q# 4, compute;
i. Geometric mean
ii. MAD from Median

iii.P73

Draw Histogram and Frequency Polygon on graph paper only
8-10
Daily wages (Rs.)
4-6
6-8
1 0 - 12
13
182
No. of employees
111
105

12-14
19

14-16
7

Make a frequency distribution table using 10 as the class-interval and start first-class from 130
onwards:
WEEKLY EARNINGS OF 50 MANUFACTURING WORKERS, IN DOLLARS
151
211
182
148
209

179
193
163
205
206

163
194
180
158
187

142
198
155
195
163

180
187
178
192
131

195
164
209
184
202

150
188
172
174
137

206
175
208
161
179

194
198
190
199
200

343
216
185
165
156

Page I o f 2

1

Q.8

(a) An investor thinks the probability that stock A will rise in price is 0.7 and the c o r r e s p o n d ^
probability for stock B is 0.4. The probability that both prices will rise is 0.3. Write the symbolic rule
for, and calculate the probability that, A or B will rise, (b) Using A, B, A ' , and B ' as classifications,
make a complete table of probabilities (c) The answer to (a) is the sum of the probabilities of what
joint events? (d) Verify that P(A or B) = 1 - P(A13'). Why would this relationship always hold for
two events?

Q.9 a) A contractor has bid on two contracts, A and B. The probability of winning A is assessed at 0.5 and
the probability of winning B if A is won is 0.7. Write the symbols for the rule, and compute the
probability that the company wins both contracts,
b) A contractor bids on two contracts A and B, assessing the chances of winning at 0.5 and 0.6 for A
and B, respectively, and the chance winning both at 0.2. What is the chance of winning A or B?
Q.10

Following Table shows the binomial distribution for n = 4 and p = 0.3.
r

0

2

3

4

P(r)
0.2401 0.4116 0.2646
0.0756
0.0081
Compute Mean and Variance of the Binomial Prob-distribution.
Q.I la) An area has hurricane once in 10 years, on the average, and the hurricane arrivals are a Poisson
process. What is the probability that in the next four years there will be (a) exactly one hurricane? (b)
at least two hurricanes?
b) Five of the 24 seemingly identical diamonds on display at Short's Jewelers are of excellent (flawless)
quality, and the remainder have slight imperfections. Jan Long purchased four randomly selected
diamonds to store in a safe-deposit box as an investment. Compute the probability distribution for
the numbers of excellent diamonds Jan purchased.
Q. 12

Using the normal approximation of the binomial. Fifty-three percent of the stockholders in Bim, Inc.,
are in favor of a mergers with Big Deal, Inc. What is the probability that in a sample of 100
stockholders less than half will be in favor of the merger?

Q.I3

Assuming mileages obtained by a certain brand of tire are uniformly distributed with a mean of
25,000 miles and a range of 10,000 miles, (a) what are the upper and lower limits of tire mileages?
(b) What is the probability that a tire will last 26,000 miles or more.

Q.14

Bill Peters has observed that when he leaves the office at the end of the day, he has to wait an
average of 4 minutes to get an elevator. Assume elevator arrivals are a Poisson process, (a) What is
the value of V? What is the unit of time? (b) What is the probability that Bill will have to wait from 2
to 4 minutes for an elevator? (c) What is the probability that Bill have to wait more than 8 minutes
for an elevator?

Q.15

A population consists of 5 elements 2, 4, 6, 8,10. Draw all possible samples of size 3 and compute;
i. Mean of samples
ii. Determine the sampling distribution of means.
iii. Compute Mean of Means and verify that

Page 2 o f 2

PRESTON

TERMINAL

UNIVERSITY
Student Name:

Course Code:
Course Title:
Program:
Semester:

iiSamabtid - Kohat - Peshawar - Lahore
U e g . No:_

QM 4354
Business Statistics
MBA/MS-IT
Fall 2010

This is a three-hour examination and consists of review questions and problems.
You may attempt not more than a total often review questions and problems.
;

PRESTON
UNIVERSITY
LIBRARY

Q.l a) Distinguish between statistics plural and statistics singular.
b) What is the d i s s interval for a frequency distribution which has classes 0.00 - 24.99, 25.00 - 49.99,
and soon.
Q.3

For the data in table below, make a frequency distribution table:
151
211
182
148
209

179
193
163
205
206

163
194
180
158
187

142
198
155
195
163

180
187
178
192
131

195
164
209
184
202

150
188
172
174
137

206
175
' 208
161
179

194
198
190
199
200

143 .
216
185
165
156

Q.4

A truck carried 22 tons of cargo a distance of 300 miles. Operating expanses (driver, gas etc.) were
$190. Compare operating expenses per ton-mile.

Q.5

Use table hi Q#2 and make a Stem and Leaf Table and write the data in ordered form.

Q.5

Define Class Mark. Fill the table with class marks.
Output per.
per Labor Hour
4.0-4.9
5.0-5.9
6,0 - 6.9
?.0^7.9
8.0-8.9
9.0-9.9

Class Mark (?)

!

No. of Days
11
17
16
8
5

Q.6

Last month an investor acquired 500 shares of a stock at an average price.'of $42 per share, tiiis
month the investor bought 300 shares of the stock at an average price of $36 per share. Find the
average price per share paid during the 2 months.

Q.7

Mdrith-to-rrionth changes in the prices of a stock were 11, 18, and — 15 percent. Using the geometric
meah.of the growth factors, determine the average monthly parentage change in the price of the
stock!
'
'

Q.8

608 employees of a firm were asked if they would favor cutting their lunch hour by VV.hour so that
they eoutd leave work that much earlier. The results are shown in the following table:
Favor (P)
. Disfavor (D)
Neutral (N)
"
Men(M) .
84
.12 - .
.24
Women(W)
204 ;
180 ,
. . 96
If a randomly selected employee is a man, what is the probability that he is neutral?
Page I o f 2

Q.9

The probability of finding oil in an area is 0.15 if the underlying stratum has a dome structure. What
is the probability of hot finding oil if there is a dome structure?
;

Q. 10

If we toss two fair coins simultaneously what is the probability of getting exactly one Head?

Q.I 1

If 60 percent of the voters in a large district prefer candidate Jordan, what is the prfcbability.that in a •
sample of 12 voters exactly 7 will prefer Jordan.

Q.12

A filling machine is set to pour 592 ml of water into bottles. The amount of fill is normally
distributed 'with a mean of 592 ml and a standard deviation of 4 ml. Use standard Normal tale to find
the probability that a bottle contains between 952 and 956 ml.

Q.13

Assume that the diameters of the shafts made by an automatic machine are normally distributed with
a p. = 25 and a = 0.5?mm. What is the probability that a shaft will have a diameter between 25.2 to
25.9 mm?

Q.J 4

The weight of maple sugar obtained by boiling down a tank of maple-tree sap is uniformly
distributed with the mean of 10 pounds and range of ) .8 pounds.
i. What are the smallest and largest weights of sugar obtained from a tank of SBp?
ii. What is the probability that a tank of sap boil down to between 9 and 10.5 pounds?

Q.I 5

How many samples of size 4 can be drawn from the population 0, 3, 6, 3,18? Compute the sampling
distribution of the mean.

fN

>*»

Page 2 of 2

U n i t s Uu£iir"Hii

TERMINAL
EXAMINATION

PRESTON
UNIVERSITY

*^SaS^6*

Kohat

-

Islamabad

-

Lahore

-

Peshawar

-

faisalabad

QM 4354
Business Statistics
MBA/MS
Summer 2010

Course Code:
Course Title:
Program:
Semester:

This is a three-hour examination and consists of review questions and problems.
You m a y attempt not more than a total of ten review questions and problems.
Define any five of the following and cite examples:
i. Error
ii. Non-Mntually Exclusive Events
iii. Mode
v. Sample Space

Q.l

iv. Statistical Inference

During a month when a scheduled 500-mile flight was token on 25 days by a plane having 240 available
passenger-seats, 60 percent of the seats, on the average, were occupied. Passenger operating revenue for the
period was $100,818. Compute revenue per passenger-mile.
b) Sales which actually totaled 9100 units for the current month had been predicted earlier at 10,000 units.
Compute the percent error.

Q.2a)

Q.3

Make a frequency distribution table using 9.0 as the class-interval and start first class from 130 onwards.

151
211
182
148
209
Q.4

179
193
t63
205
206

163
t94
180
158
187

250 - 274
275 - 2 9 9
300-324
325-349
350-374
375-399
•1110 - 424
425-449 •
4 5 0 - 474i '
4*5-499'
:

;

:

Q.6

180
187
178
192
131

195
164
209
184
202

150
188
172
174
137

From tha table given below compute; i. MAD from Mean
Rent. Dollars per month

Q5

142
198,
155
195
163;

206
175
208
161
179

194
198
190
199
200

143
216
185
165
156



ii. Coefficient of Variance

Numbers of apartments
8
23
52
86
63
56
37
26
11
7

Compute Mode, Median and Geometric Means from data given below*
2 3 / 1 1 , 40, 35, 69, 75, 80, 105, 36, 8

'

The probability* of finding oil m an area where the underlying rock formation has 4 dome structure
is 0.3. gasedupon soundings,'a geologist states the probability that a dome structure exists is 0:8.
(a) What is the probability that the dome structure exists and oil will be foitrnd? (b)Using F and D,
respectively, for find oil and dome exists, write the relevant symbolic probability rule for (a)'

Page 1 of 2

I
Q.7

If A and B ate independent wilh P{A) = 0.3 and P(B) = 0.4, calculate P{A or B). Explain the
method used.

Q.8

If a coin is tossed 20 times (a) What is the expected number of heads? (b) What is the probability that the
number of heads will turn out to be the expected number?
';

Q.9

If 04 percent of a bank's account balances are in error and a sample of 200 accounts is selected, find the
probability that (a) none of the 200 balances is in error, (b) exactly one balance is in error; (c) at least three
balances arcin error; (d) the number of balances in error is from two to five, inclusive; (e) fewer than •four
balances are in em». i
:.

Q.10

In an audit of accounts of Jordan-HoKman, a large department store, it is decided Qist to check a sample of
1000 accounts, and tHen to carry out a more detailed study if the number of sample accounts in error exceeds
15. One percent of alf Jordan-Holtnian accounts contain errors. What is the probability that the sample audit
results will lead to a more detailed study?

Q. 11

Suppose that the weight of maple sugar obtained by boiling down a tank of ample-tree sap is uniforhiry
distributed with a mean of 10 pounds and a range of 1.8 pounds, (a) What are the smallest and largest
weights of sugar obtained Irom a tank of sap? What'is the probability that a tank of sap will boil down to
between 9 and 10.5 pounds? '

Q.12

The cylinder-making machine has o = 0.5 mm. At what mean value JJ. should the machine be set to ensure
that only 2.5 percent of the cylinders have diameters of 2 5 . 4 8 mm or more?

Q.13

A population consists of five elements 2,3, 6, 5,10. Draw all positive samples of size 3.
i. Compute the proportion for even numbers
ii. Make a sampling distribution of proportions and verify that
a. u -

Q.14

=P

b-

Using table given below, draw i. Histogram
graph paper only.
Out put per labor-hour
4.0^1.4
4.5-4.9
5.0-5.4
5.5-3.9
6.0-6.4
6,5-6.9
7.0-7.4
7.5-7.9
8.0-8.4
8.5-8.9
9.0-9.4
9.5-9.9

Q. 15

ii; Cumulative frequency polygon (Topped-Bottom). On

Number of days
1
3
8.
6
11
9
7
5
3
4
1
Frequency total 60~*

Define and give examples:
i. Class — Boundaries
ii. Geometric mean
iii. Statistics in the plural sense
iv. Simple random sample.
Page 2 of2

PRESTQM '

i w v i i i - ^

UNIVERSITY
Kohat

-

Course Code:
Course Tide:
Program:
Semester:

EXAMINATION

Islamabad

-

Lahore

-

Peshawar

-

Faisalabad

QM43S4
Business Statistics
MBA/MS
Summer 2009

This U a three-hour examination and consists of review questions and problems.
You may attempt not more than a total of ten review questions and problems.
Q. 1

Define any FOUR of the following with examples:
i. Error
ii. Class-interval
iii.Mutually exclusive events
iv. Sample-Space
v. Dependent-Events
vi. Population and Sample

Q.2 a) Distinguish between statistics plural and statistics singular,
b) What is a simple random sample?
c) With what type of decision is statistical decision analysis concerned?
Q.3 a) Prom the data given in the following table, present a tabular comparison cf the percentage distribution of
sales by region for the 2 years. Round to the first decimal place:
Sales, thousands of dollars
Region

This year

Last year

East •
Central
West

$2465
2084
1391

$2415
1814
998

b) Round the following to three significant digits (a) 408.52; (b)0.036972; (c)237,401,62; (d) 1.065;
(e) 1.055; (f) 24,449.
Q.4

Q.5

UaingihetabIeofQ#6 Draw
i. Histogram ' •
ii. Cumulative frequency polygon (Topped to Bottom)

'

1

Make ajfrequency table using 8,0 as the lower limit of the first class and with a width of 1 unit, convert it to
a frequency distribution:
>
'
9.0

4t.fi
*1,7
10.1
12.3
10,5

10.2
13.6 11:0 '
14,1.
9.8
13,2

U.3
16.4
8.0
10.0
13.0
10.S

12.1
11.0
12.0
9.9
9.1
106

10.7
15.8
11."5
tt.4
8.3
12.5

13.8
9.3
9,7
15.7
12.9
15.1

. 10.8
13.7
11.6
11.5
14.0
12.8

Page ] oF3

Q6

Using the taple given below, compute;
i.C.V
ii.IQR
iii. P and D
63

Rent, Dollars;per mouth
250-274
275-299
300-324
325-349
350-374
375-3*19
400 - 4 2 4
425-449
450 -414
475-499

Q.7

3

Numbers of apartments.
6
23
52
36
68
56
37
26
11
7

From the table given below compute: i. MAD from Median
TABLE: ;
Frequency Distribution for output per labour-hour

ii. Geometric Mean
,

iii. Moote
*

Output per labor hour Number of days
4.0 - 4.4
1
2
4.5-4.9
5.0-5.4
3
5.5-5.9
8
6.0-6.4
6
6.5 - 6.9
n
7.0-7.4
9
7.5-7.9
7
8.0-8.4
5
8.5 - 8.9
3
9.0-9.4
4
9.5-9.9
1
Frequency total: 60
Q.8

The probability of finding oil in an area is 0.15 if the.underlying stratum has a dome structure.. What is the
probability of not finding oil if there is a dome structure?

Q.9 a) KP(Q/S) = 0.25 &ndP(QS) = Q.l, find P(S).
b) Let B,R'Q, O'be two events and their complements, (a) What joint event constitute R of Q7 (b)Whatis
the complement of R or g ? (c) Complete the following: P{R or g ) = 1 - P( >.
A motel has 45 rooms available on a particular night. In as much as 10 percent of the large population of
those making motel reservations fail to show up, the motel makes 50 reservations for tliis particular night
Use the binomial distribution to find the probability that rooms will be available for all those who do show
up.

One percent of the oysters found by native divers off Palm Tree Atoll contain a pearl. If Captain Cruiser
buys 40 Oysters, what is the probability that he will obtain at least three pearl-bearing Oysters?
Q.lla) A bird arose early one morning and ate five of the 20 cherries remaining on a cherry tree,. Four of the 20
cherries contained a worm. What is the probability that the early bird got three or more worms?
b) An area has a hurricane once in 10 years, on the average, and hurricane arrivals are a Poison process. What
is the probability mat in the next 4 years there will be (a) exactly one hurricane? (b) at least two hurricanes?
Pago 2ot3

]

1

Q. 12

Assuming mileages obtained by a certain brand of tire are uniformly distributed with a mean of 25,000
miles and a rang of 10,000 miles, (a) what are the upper and lower limits of tire mileages? (b) what is the
probability that a tire will last 26,000 miles or more?

Q.13

Fordbart Casualty Co. insures a large number of buildings for fire damage. On the average, Fordhart lias to
pay eight-damage claims of over$l million each year. The Company is short of cash and will have to sell
some of its securities to get cash if it has to pay a damage claim of more than $1 million during the next 3
months. Assuming damage claims over $1 million are a Poisson process, what is the probability that the
Fordhart will have to sell securities.

Q.14

Some people who make reservations for air travel do not show up for their scheduled flight. Airlines may
make allowances for these "no shows" by booking reservations for more persons than can be accommo­
dated on a flight. If 4 percent of the large population of reservations turn out to be no-shows, and 350
reservations are made for a particular flight on a plane seating 340, what is the probability that seats will be
available for all those who do show up for the flight?(UseNAB to solve)

Q.15

A population consists of 6-elements 0,3,6,7,10,13,
i. Draw all possible samples of size 3.
ii. Make a Sampling Distribution of proportions using odd numbers as a success,
iii. Verify that;

fPQ

Page 3 of 3

TERMINAL
EXAMINATION

•RKSTON
NIVERSITY
hut
Islamabad

-

Lahore

-

Peshawar

-

Paisalabad

QM 4354
Business Statistics
MBA/MS
Summer 2008

Course Code:
Couise Title:
Program:
Sem :ster: ,

Thls-is a i h r e V h o u r examination and consists of review questions and problems.
You may attt mpt not more thnn a total of ten review questions and problems.
Q. I a)
b)
c)

Diatin] ulsh between statistics plural and statistics singular.
What i i the a simple random sample?
What, k a statistical inference?

a. A pi ice of $99.95 is to be reduced by 20 percent. Show two ways to compute the new price b. Sales this
year ai E $20,900 compared with $22,000 last year. Compute and describe the percent change in sales form
last ye IT to this year.
b) Use Tible given below to compute percentage relatives. Round to the first decimal place, (a) Take period 1
equal ip 100 (b) Take the average of periods 1 and 2 = 100
TABIC
~~2~
1
4
Peri
3
73.9
77.9
8.9
Price, cents per gallon
83.9

Q.2a)

Q.3

Make a frequency table using 21 as the class-interval and start first class-from 85-105.
165
156
136
Hi
9

O

186
114
127
90
170

122
113
112
187
111

172
135
188
136
147

140
131
171
159
165

153
125
179

208
177
152

103

T59~

169
136
155
8_5_
150

Q4

Using he table of #6, draw Cumulative frequency polygon (Topped -Bottom) and Histogram.

Q.5

The c< sts per load (in cents) of 35 laundry detergents tested by a consumer organization are shown below
Table
CI iss Limits
13-19
; 10-26
27-33
'14-40
H -47
*8-54
S5-61
52-68
Cornp rie:
i. C.V.
li. I Q l
iii. MAD from Median

2
7
12

5
6
1
0
2

Q.6

Using table given below representing light bulbs to determine their life times (in - hows). Compute i.
andFjTv
ji. Moic
iii. Geometric mean
iv. Average
Class - Boundaries
52.5 - 63.5
63.5- 74.5
7 4 . 5 - 85.5
85.5-96.5
96.^-107.5
107.<S-118.5

6
12
25
18
14
5

Q.7

The probability that it will be colder tomorrow is 0.6 and the probability it will snow if it gets cojder is 0.7.
What is the probability that ii will colder and snow tomorrow?

Q.8

A tire Supplier has 10 tires in stock. Although they ali look alike, two of them are retreads and eight are
new. (^) If a buyer selects two at random, what is the probability that both are new? Both retreads? (b) If a
buyer Selects four, what is the probability that at least one is a retread?
:

i

Q.9 a)

A secretary types' 75 words per minute and averages six errors per hour of typing. Assuming error
occurrences ore a Poisson process, what is the probability that a 225-word letter will be typed without error,
b) Threelpercent of the large number of tires made by a manufacturer are defective. If a store buys 100 of
these tires, what is the probability that the number of defectives received is (a) zero? (b) less than three*? (c)
more than six7
i

Q.10

The probability of success on a binomial trial is 0.10. Porn •= 50 trials, find the probability that the number
of successes will be (a) less than five; (b) at least five; (c) at most five; (o) more than three; (e) a[ least two,
but less than seven; (f) form zero to five, inclusive;(g) exactly six, (Iv) at least 10.

Q.ll

If 55 percent of the voters in an area favor a particular candidate, what is the probability that, in a sample
of200] voters, less man half would favor the candidate?Note: (Use NAB to solve Q# 11).

Q.I2

A random variable takes on values symbolized by x. If the available is normally distributed with a mean of
50 arid a standard deviation of 4 what is the probability that x will be in the following intervals?- •
i. 50 to 54
ii. 45 to 54
iii. 53 to 58
iv. more than 60
v. less than 45
vi. more than 45

Q.13a) Assuming mileages obtained by a certain brand of tire uniformly distributed with a mean of25,000 miles
andafange of 10,000 miles (a) what are the upper and lower limits of tire mileages? (b) What is the
probability that a tire will last 26,000 miles or more7
b) Bill Peters has observed that when be leaves the office at the end of die day. lie lias to wait an average of 4
minutes to get an elevator. Assume elevator arrivals are a Poisson process- (a) What is the value of X? What
is the unit of time? (b) What is the probability that Bill will have to waif, from 2 to 4 minutes for an
elevator? (c) What is the probability that Bill have to wait more man 8 minutes for an elevator?
Q.I4

A population consists offive elements 2,3,5,6 and ! 1.
i. Draw all possible samples of size 3 (without replacement).
ii. Compute the prnrje/l^es for odd nnmbws.
iii. Make a sampling distribution of properties and verify that
a. u - -P
;
p

Q.15

.
~j

.

.
"
-

b. a - = . / — . J
"
If n
VjJV-1

Define any FOUR of the following;
i. Sample - space
ii. Mutually Exclusive Events
iii. Enoi
v. Dependent - Events
vi. Discrete ad Continuous Variables.

iv. Subjective - Probability

PRESTON

TERMINAL

UNIVERSITY
^ j ^ ^ ^ g ^

Kohat -

Islamabad -

EXAMINATION
Peshawar — Lahore -

Faisalabatl — Multan — Gujrmiwala

Q M 4354
Business Statistics
MBA/MS
Fall 2007

Course Code:
Course Title:
Program:
Semester:

This Is a three-hour examination and consists of review questions and problems.
You may attempt not more than, a total of ten review questions and problems.
Q.l

Explain any FOUR of the following:
i. Statistical Inference
ii. Decision Analysis
iii. Sample Random Sample
iv. Population and Error
v. Uses of Statistics

Q.2 a) Compute percentage relatives for the board feet prices in the following Table. Round to the first
decimal place.
i. Take period 2 as 100.
ii. Take the average of periods 1 through 3 as 100.
TABLE:
Period
Price per 1000 board feet

1
2
£130.25
$154.98

3
$174.35

4
$150.62

5
$125.63

b) Unemployment at the end of a year was 7.1 percent of the civilian labor force. At the beginning of
• year it; had been predicted that die figure would reach 7.4 peicent by the year's end. By how much was
the prediction in error i. In percentage points
ii. In percent?

————
Q.3

Draw Histogram and Frequency Polygon from the following Table.(Use graph paper only).
TABLE
Rent, dollars per month
No of apartment
..

2^0-274
275 - 299
300-324
325 - 349
3S0-374
375 - 399
400 - 424
4iS - 449
;
4^0-474
. 475 - 499
Q.4

'8'
23
52
86
68
56
37 .
26 .
11
7

Mafctf a frequency table using 5.0 as the class-interval and start first class rrom48.0 - 52.0 onwards
71.6
81.9
77.8
48.6

95.5
68.9
69.4
83.5

73.0
74.2
S3.2
70.8

74.2
80.7
82.7
72.1

81. S
65.7
73.S
71.6

90.6
67,6
64.2
59.4

55.9
82.<t
63.9
77.6

Q.5

From the follow table compute

.

Q.6

Weight

f

65-84
85-104
105 - 124
125 - 144
145-164
165-184
185 - 204

9
10
17
10
5
4
5

i. Mad from Median

ii. Geometric Mean

iii. iQR

Using the Table of Q#5, compute;
i. Coefficient of Variance
ii. Mode
iii. D.i and P
61

Q.7 a) In a firm, 20 percent of the employees have accounting back grounds, while 5 percent of the
employees are executives and have accounting backgrounds. If an employee has an accounting
background, what is the probability that the employee is an executive?
b) A contractor has bid on two contracts, A and B. The probability of winning A is assessed at 0.5 and
the probability of winning B if A is won is 0.7. Write the symbols for the rule, and compute the
probability that the company wins both contracts.
Q.S

Compute Mean and Standard Deviation form the following table;
'r
" >(r)

0

1

0.2401 0.4116

~~T~
0.2646

3~~~
0.0756

4
0.0081

Q.9 a) Calls at a telephone switchboard follow a Poisson process and occur at an average rate of six calls per
10 minutes. The operator leaves for a 5-niinute coffee break, (a) What is the value of U7 What is the
probability thai exactly two calls come in (and so go unanswered) while the operator is away? What is
the probability that more man three calls go unanswered?
b) Oil-drilling rights at. 25 sites on government-owned property have been sold to oil companies. The
sites are to be assigned at random to the companies. Oil Ventures, Inc, which has purchased leases for
four sites, has a preference for three of the 25 sites. What is the probability that Oil Ventures gets at
least two of its preferred sites?
Q. 10

A test has 25 true-false questions. A student flip's a coin for each question and checks true if heads
show and false if tails show. If 1 7 or mote correct is passing, what is the change that this student will
pass?
Use Normal Approximation of Binomial (NAB).
• .

. Q. 11

Suppose taxicab arrivals from 3 to 5 p.m. are a Poisson process. If the cabs arrive at an average rate of
18 per hour, what is the probability that a person will have to wait up to 5 minutes for a cab7

Q.12

A random variable takes on values symbolized by x. Jf the available is that normally distributed with a
mean of 1000 and a standard deviation of 100 what is the probability that x. will be in the following
intervals? (Make a normal curve sketch for each)
"" " — ~"
i,1000 to 1155
ii. I 0 S 0 t o H 4 0
iii.925 to 1075
iv. Less than 865

0.13

!

A population consists of five elements 0,2, 4, 5 and 11. Draw ail possible samples of size 3 ' .
Compute Sample proportion for Even number. Make a sampling distribution of proportion and verify
that:
a.
b.

Q.I4

For n = 50, p = 0.01, find from the cumulative tables; n. the binomial probability of fewer than three
successes; b. the Poisson probability of fewer than three,successes; c. the difference between the
answers to (a) and (b); d. What rule of thumb does the foregoing illustrate?

0.15

Explain the following:
i. Sample space
ii. Class-width
iii. Mutually and Non-mutually exclusive events
iv. Conditional probability

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