Q1: A light bulb manufacturer claims that less than 5% of his bulbs are defective. When 1000 bulbs were drawn from a large production run, 1% were found to be defective.

a. What is the population of interest?

b. What is the sample?

c. What is the parameter?

d. What is the statistic?

e. Does the value 5% refer to the parameter or to the statistic?

f. Is the value 1% a parameter or a statistic?

g. Explain briefly how the statistic can be used to make inferences about the parameter to test the claim.

Question 2

A large university campus has 60,000 students. The president of the students' association wants to conduct a survey of the students to determine their views on an increase in the student activity fee. She would like to acquire information about all the students but would also like to compare the school of business, the faculty of arts and sciences, and the graduate school. Describe a sampling plan that accomplishes these goals.

Question 3

A large investment firm in Sydney wants to review the distribution of the ages of its stockbrokers. The firm feels that this information will be useful in developing plans relating to recruitment and retirement options. The ages of a sample of 25 brokers are as follows:

51	64	32	55	41	44	24	46	58	47	36	52	54
44	66	47	59	51	61	57	49	28	42	38	45

1. Constructafrequencydistributionforthedata,usingfiveclassintervalsandthevalue20asthelowerlimitofthefirstclass.
2. Construct a relative frequency histogram for the data, using five class intervals and the value 20 as the lower limit of the first class.
3. Construct a frequency polygon.
4. Construct an Ogive for the data.
5. What proportion of the total area under the histogram from part (c) falls between 20 and 40?
   1. What proportion of the investments had a return of between 10% and 30%? What proportion of the investments had a return of between 10% and 50%?

Question 4

Last year, the rates of return on the investments in a large portfolio had an approximately mound-shaped distribution, with a mean of 20% and a standard deviation of 10%.

1. What proportion of the investments had a return that was either less than 10% or more than 30%?
2. What proportion of the investments had a positive return? (Hint: A mound-shaped distribution is symmetrical.)

Question 5

An international aerospace company has submitted bids on two separate federal government defence contracts, Aand B. The company feels that it has a 60% chance of winning contract Aand a 30% chance of winning contract B. If the company wins contract B then the company believes it has an 80% chance of winning contract A.

1. What is the probability that the company will win both contracts?
2. What is the probability that the company will win at least one of the two contracts?
3. If the company wins contract B, what is the probability that it will not win contract A?
   1. What is the probability that the firm's sales will exceed $3 million?

Question 6

A marketing manager of a leading firm believes that total sales for the firm next year can be modelled by using a normaldistribution with a mean of $2.5 million and a standard deviation of $300 000.

1. What is the probability that the firm's sales will fall within $150 000 of the expected level of sales?
2. In order to cover fixed costs, the firm's sales must exceed the break-even level of $1.8 million. What is the probability that sales will exceed the break-even level?
3. Determine the sales level that has only a 9% chance of being exceeded next year.