2. A department store has determined that 36% of all their sales are credit sales. A random sample of 65 sales is selected.

(a) Explain the distribution of the sample proportion of the credit card sales.

(b) What is the probability that the sample proportion will be greater than 0.40?

(c) What is the probability that the sample proportion will be between 0.30 and 0.40?

(d) What is the probability that the sample proportion will be less than 0.30?

3. The number of television sets produced daily from an assembly line is normally distributed with a mean of 430 sets and standard deviation of 20 sets. For 30 randomly selected days of the production line

(a) Construct a 95% confidence interval for the population mean number of sets per hour?

(b) What is margin of error used in (a)?

(c) What sample size should be taken so that a 95% confidence interval will have a margin of error less than 16 sets per day?

4. In a survey of 600 personnel directors, 40% thought that they would be hiring new personnel over the next three months.

(a) Construct a 97% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?

(b) What is margin of error used in (a)?

(c) Find the necessary sample size, if they wish to be accurate within 3% of the true proportion.