2. Suppose we want to study the errors found in the performance of a simple counting task (i.e., counting the number of defective parts per year, etc.). Some managers will count too few defective parts, and other managers will count too many defective parts. Suppose we find that, across managers, the mean number of defective parts reported is 975 with a standard deviation of 15. Assume that the distribution of counts is normal.

2a. What percentage of the counts will lie between 960 and 990?

2b. What percentage of the counts will lie below 975?

2c. What percentage of the counts will lie below 990?

2d. Which two values of X (the count) would encompass the middle 50% of the results? Round the results to the nearest integer.

2e. 75% of the counts would be less than _______. Round the results to the nearest integer.

3. A dean must distribute salary raises to her faculty for next year. She has decided that the mean raise is $2,000, the standard deviation of raises is to be $400, and the distribution is normal.

3a. The most productive 10% of the faculty will have a raise equal to or greater than $_____.

3b. The 5% of the faculty who have done nothing useful in years will receive no more than $_____.

4. A minibar in a hotel room generally provides an impression that the hotel is more upscale. PKF Hospitality research reported that minibars provide a mean annual revenue of $368 per hotel room (USA Today, February 9, 2012). Consider an upscale hotel in San Antonio, Texas, that has a total of 330 rooms, each with a minibar. Assume that the total monthly revenue for this hotel's minibar service is normally distributed with a standard deviation of $2,200.

4a. Using the mean annual revenue of $368 per minibar, what is the mean monthly revenue for the minibar service from all rooms at this hotel?

4b. What is the probability that the monthly minibar service provides over $12,000 in revenues for this hotel? (3 pts; Hint: Please conduct your analysis based on monthly revenue for ALL minibars, not one minibar.)

4c. What is the probability that the monthly minibar service provides less than $7,500 in revenues for this hotel? (3 pts; Hint: Please conduct your analysis based on monthly revenue for ALL minibars, not one minibar.)