Question: A chain of audio/video equipment discount stores employs 36 salespeople. Daily dollar sales for individual sellers employed by the chain have a normal distribution with a mean of $2,000 and a standard deviation equal to $300.

1. Suppose that the chain's management decides to implement an incentive program that awards a daily bonus to any salesperson who achieves daily sales over $2,150. Calculate the probability that an individual salesperson will earn the bonus on any particular day.
2. Suppose that (as an alternative) the chain's management decides to award a daily bonus to the entire sales force if all 36 achieve an average daily sales figure that exceeds $2,150. Calculate the probability that average daily sales for the entire sales force will exceed $2,150 on any particular day.
3. Intuitively, do you think it would be more difficult for an individual salesperson to achieve a daily sales figure that exceeds $2,150 or for the entire sales force of 36 to achieve an average sales figure that exceeds $2,150 ? Are the probabilities you computed in parts a and b consistent with your intuition? Explain.
4. Sketch the distribution of individual daily sales figures and the probability you computed in part a. Place values that are three standard deviations above and below the mean in the tails of the distribution. Also sketch the distribution of all possible sample means (the sampling distribution of \(\bar{x}\) ) and the probability you computed in part b. Place values that are three standard deviations of \(\bar{x}\) above and below the mean in the tails of the sampling distribution. Compare the sketches. Do you see why the results in parts a and b turned out the way they did? Explain why.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document