Revision Programme- Business Statistics- 2015
(1) The grades of 10 students on their first management test are shown below.
94
61
96
66
92
68
75
85
84
78
a.
Construct a frequency distribution. Let the first class be 60 - 69.
b.
Construct a cumulative frequency distribution.
c.
Construct a relative frequency distribution.
(2) A sample of 9 mothers was taken. The mothers were asked the age of their oldest child.
You are given their responses below.
3
12
4
7 14 6 2
9 11
a.
Compute the mean.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
f.
Determine the median
h.
Determine the range.
3. The amount of coffee dispensed by a vending machine is assumed to be normally distributed.
The vendor claims that the mean amount of coffee dispensed by the machine is at least 6
ounces per cup. The office manager doubted this claim. She randomly selected twenty-four
cups of coffee from this machine and recorded the amount of coffee in each. The sample mean
was 5.8 ounces with a standard deviation of .8 ounces. Do the data provide sufficient evidence
to indicate that the mean amount of coffee dispensed is less than 6 ounces per cup? Use a =
.01.
4.A life insurance salesman sells on the average 3 life insurance policies per week. Use Poisson's
law to calculate the probability that in a given week he will sell
a. Some policies
b. 2 or more policies but less than 5 policies.
c. Assuming that there are 5 working days per week, what is the probability that in a given day
he will sell one policy?
5. Twenty sheets of aluminum alloy were examined for surface flaws. The frequency of the
number of sheets with a given number of flaws per sheet was as follows:
Number of flaws Frequency
0
4
1
3
2
5
3
2
4
4
5
1
6
1
What is the probability of finding a sheet chosen at random which contains 3 or more surface
flaws?
6.
Vehicles pass through a junction on a busy road at an average rate of 300 per hour.
a. Find the probability that none passes in a given minute.
b. What is the expected number passing in two minutes?
c. Find the probability that this expected number actually pass through in a given twominute period
7.
Dr. Tillman is Dean of the School of Business Socastee University. He wishes prepare to a report
showing the number of hours per week students spend studying. He selects a random sample
of 30 students and determines the number of hours each student studied last week.
15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3,
29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.
8.
Mr. Jayatissa wishes prepare to a report showing the number of hours per week students
spend studying. He selects a random sample of 30 students and determines the number of
hours each student studied last week
15.0, 23.7, 19.7, 15.4, 18.3,
23.0, 14.2,
17.4, 18.6, 12.9, 20.3, 13.7,
21.4, 18.3, 29.8, 17.1, 18.9,
10.3, 26.1, 15.7, 14.0, 17.8, 33.8,
20.8, 13.5, 20.7,
23.2, 12.9, 27.1, 16.6.
Organize the data into a frequency distribution.
9.
During a one hour period on a hot Saturday afternoon cabana boy Chris served fifty drinks. He
sold five drinks for $0.50, fifteen for $0.75, fifteen for $0.90, and fifteen for $1.10. Compute
the weighted mean of the price of the drinks.
A sample of five executives received the following bonus last year ($000):
14.0, 15.0, 17.0, 16.0, 15.0
Compute the arithmetic mean ?
10.
The following frequency distribution reports the number
50 sections of various
of students enrolled in each of the
courses taught in the College of Business last summer.
Students
Frequency
0 up to 10
3
10 up to 20
8
20 up to 30
16
30 up to 40
10
40 up to 50
9
50 up to 60
4
Total
50
Determine the mean number of students per section.
Determine the median number of students per section
11.
A Nescafe machine is adjusted to fill 30ml cups. However, it has a probability of 0.25 of
over filling a cup. In a function 25 participants were requested Nescafe, so that 25 cups were
filled using the machine. Find the probability that,
i. No cups will overfill
ii. At most two cups will overfill
12.The coordinator of a Diploma program claims that 80 percent of the candidates who
complete the program successfully got employed. This year a group of 15 students joined the
program completed successfully.
Find the probability that
i. All of them got employed
ii. None of them got employed
iii. At least 10 of them got employed
13.
A firm producing small electric resisters claims that they will not allow more than 0.75
amperes to pass by under normal conditions. However, when a sample of 32 resisters was
tested, it was found that the average amperes allowed through them is 0.9 amperes. Test
the manufactures claim at 10% level assuming the population variance is 0.5 amperes.
14.
In an attempt to test whether or not a special training program has improved the productivity
of the employees in a company, a sample of 25 employees were selected and the time taken to
do a particular job after the training was measured. The average time required to do the
job by these trained employees was calculated as 18 minutes. The time required to do the same
type of a job by an untrained employee is 20 minutes with a standard deviation 16 minutes.
Test whether the training was able to reduce the time to do the job significantly.
15.
The following data elements represent the amount of time (rounded to the nearest second)
that 30 randomly selected customers spent in line before being served at a branch of First
County Bank.
183 121 140 198 199 90 62 135 60 175 320 110 185 85 172 235 250 242 193 75 263 295 146
160 210 165 179 359 220 170
(a) Develop a frequency distribution for the above data.
(b) What are the lower and the upper class limits for the first class of the above frequency
distribution?
(c) Develop a relative frequency distribution and a percent frequency distribution for the above.
(d) Develop a cumulative frequency distribution
(e) How many people waited less than or equal to 239 seconds?
(f) Develop a cumulative relative frequency distribution and a cumulative percent frequency
distribution.
(g) Construct a histogram for the waiting times in the above example.
(h) Construct an ogive for the above example
15.
The following table gives information on ages and cholesterol levels for a random sample of 10
men.
Age 58
69
43
39
63
52
47
31
74
36
Chole 189 235 193 177 154 191 213 165 198 181
sterol
level
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Taking age as an independent variable and
cholesterol level as a dependent variable,
compute SSxx, SSyy, and SSxy.
Find the regression of cholesterol level on
age.
Briefly explain the meaning of the values of
a and b calculated in part b.
Calculate r and r2 and explain what they
mean.
Plot the scatter diagram and the regression
line.
Predict the cholesterol level of a 60-year-old
man.
Compute the standard deviation of errors.
Construct a 95% confidence interval for B.
Test at the 5% significance level if B is
positive.
Using α = .025, can you conclude that the
linear correlation coefficient is positive?
Thanking You…. All the very best dear Students !