**UNIVERSITY EXAMINATIONS: 2016/2017**

**EXAMINATION FOR THE DEGREE OF BACHELOR OF BUSINESS IN**

**INFORMATION TECHNOLOGY**

**BUSS305 STATISTICAL DECISION MAKING**

**SPECIAL /SUPPLEMENTARY EXAMINATION**

**DATE: JULY, 2017 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.**

**QUESTION ONE – Compulsory (Total Marks: 30)**

a) Give three reasons why researchers prefer using samples instead of the population when

collecting data. (3 Marks)

b) State and briefly discuss three properties of a good estimator. (3 Marks)

c) State two basic reasons for the need for forecast in any field. (2 Marks)

d) State the characteristics of a binomial distribution. (2 Marks)

e) Differentiate the following terms

i) Estimate and estimator (2 Marks)

ii) Point estimation and interval estimation (2 Marks)

f) A bank receives 30 applicants for a loan. The research team has established that 25% of the

businesses will file for bankruptcy in 5 years. What is the probability that 4 of the applicants

file for bankruptcy in this period? (3 Marks)

g) Let X be a normal random variable with

h) A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds

of vehicles passing through this construction zone are normally distributed with a mean of 46

miles per hour and a standard deviation of 4 miles per hour. Find the percentage of vehicles

passing through this construction zone that are travelling at speeds between 50 and 55 miles

per hour. (5 Marks)

**QUESTION TWO (20 MARKS)**

a. A publishing company has just published a new college textbook. Before the company

decides the price at which to sell the book, it wants to know the average price of all such

textbooks in the market. The research department at the company took a sample of 36

comparable textbooks and collected information on their prices. The information produced a

mean price of $ 70.50 for this sample. It is known that the standard deviation of all such

textbooks is $ 4.50.

i. What is the point estimation of the mean price of all such college textbooks.

(1 Mark)

ii. What is the margin of error for this estimate? (3 Marks)

iii. Construct a 90% confidence interval for the mean price of all such college

textbooks. (4 Marks)

b. A sample of seven households from a low income neighbourhood was selected and data on

their income and expenditure collected. The information obtained (in hundreds of dollars) is

given in the table below.

i. Find the least square regression line for the data. (9 Marks)

ii. Using this estimated regression model, find the predicted value of food expenditure

for a family whose monthly income is $ 3500. (2 Marks)

iii. Find the estimation error in your regression model. (1 Mark)

**QUESTION THREE (20 MARKS)**

a. Forecasts are vital to every business organization and for every significant management

decision. Briefly discuss five areas in which forecasting is widely used. (10 Marks)

b. You work in the Quality Control Department for Philips. A light bulb life has a normal

distribution with mean,

2000

hours and standard deviation

200

hours. What is the

probability that a bulb will last

i. less than 1470 hours? (4 Marks)

ii. between 1800 hours and 2200 hours (3 Marks)

iii. between 2130 hours and 2500 hours (3 Marks)

**QUESTION FOUR (20 MARKS)**

a. Among people in the managerial or professional occupations in Kenya, about 48% are

female. For three people selected at random from these occupations, find the probability that:

i. All three are female (3 Marks)

ii. Atleast one is female (4 Marks)

iii. None is female (3 Marks)

b. The Governor of Nairobi claims that the average net worth of families living in the city is

at least $ 300,000. A random sample of 100 families selected from this city produced a mean

net worth of $ 288,000 with a standard deviation of $ 80,000. Using a 2.5% significance

level, can you conclude that the Governor’s claim is false?

(10 Marks)

**QUESTION FIVE (20 MARKS)**

a. On average, a secretary makes two typing errors per page. Find the probability that she

makes

i. No errors (2 Marks)

ii. Fewer than two errors on the next pages she types. (4 Marks)

b. Lots of 40 components each are called acceptable if they contain no more than three

defectives. The procedure for sampling the lot is to select 5 components at random and

reject the lot if a defective item is found. What is the probability that exactly one defective

item will be found in the sample if there are three defective items in the entire lot?

(4 Marks)

c. Define the term “Decision Making”, hence state and briefly discuss the managerial decision

making process. (10 Marks)