1. The amount of time a supervisor devotes to his or her new employees to obtain high operational efficiency is a random variable that is normally distributed with an average of 7.5 hours and a standard deviation of 2.1 hours.

• What proportion of supervisors spend more than 10 hours per week for their new employees to achieve high operational efficiency?
• Find the likelihood that supervisors will spend 7-9 hours to get your new employees to achieve high operational efficiency.
• What proportion of supervisors spend less than 3 hours for their new employees to achieve high operational efficiency?

2. The number of pizzas consumed by an organization's employees per month is normally distributed with an average of 10 and a standard deviation of 3. What is the probability that a random sample of 25 students will consume more than 275 pizzas?

3. A business consultant collects the times (seconds) of the dispatch services performed by two fast food companies. The data is listed here. Can you infer that company A and company B differ in the variances of the service times they offer? Why? Perform the F test to prove it and the p-value criterion to answer the question.

Company A: 120 150 130 100 95 90 110 120 100 95

Company B: 70 90 95 250 150 100 95 99 230 95

4. An operations manager overseeing an assembly line has had problems with the sequence of jobs. The problem is that bottlenecks occur due to the inconsistency of sequential operations. You decide to perform an experiment in which two different methods are used to complete the same task. he measures the times (in seconds). The data is listed here. Can you infer that the second method is more consistent than the first method? Perform the appropriate t-test and p-value criterion to answer the question.

Method 1 8.8 9.6 8.4 9.0 8.3 9.2 9.0 8.7 8.5 9.4

Method 1 9.2 9.4 8.9 9.6 9.7 8.4 8.8 8.9 9.0 9.7