1. The amount of time a bank teller spends with each customer is normally distributed with a mean of 6.8 minutes, and a standard deviation of 2.4 minutes.
   1. (a) What is the probability that the teller will spend more than 10 minutes with a customer? Make sure to define the random variable under consideration.
   2. (b) A random sample of 16 customers is selected.
      1. (1) Specify the sampling distribution for the mean of the sample. Be sure to include the mean and standard deviation of the distribution.
      2. (2) What is the probability that the average time spent per customer will be at least 6.5 minutes?
      3. (3) There is an 80% chance that the sample mean will be at least how many minutes?
      4. (4) If the time spent per customer was not normally distributed, would the results in (2) and (3) be valid? Explain.
   3. (c) Suppose that it cannot be assumed that the time spent per customer is normally distributed. If a sample of 64 customers is selected, compute the probability that the average time spent per customer will be at least 6.5 minutes, and comment on the validity of the result.