When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of 45 minutes with a standard deviation of 6 minutes. Suppose each night, 9 deliveries are selected at random and their delivery times are recorded. For the sake of argument, assume that the pizza deliveries are normally distributed.

1) What is the probability that the average time for the sample mean each night is within 2 minutes of the population mean?

2) What is the probability that the average time for the sample mean each night is within 2.5 minutes of the mean?

3) What is the probability that the average time for the sample mean is within 4 minutes of the mean?

A study was conducted to estimate the cost of employee absences. Based on this research, the amount of paid-time lost over a 3 month period was found to be normally distributed with a mean of 1.5 days and a standard deviation of 2.5 days. A sample of 100 employees was taken, find

4) The probability that the sample mean is greater than 1.6 days?

5) The probability that the sample mean is within a ½ day of the population mean?

6) The probability that the sample mean is between 1.35 and 1.85 days?

7) Suppose a population is normally distributed with a mean of 5,000 and a standard devation of 1,000. A sample of size 100 is taken, what is the standard error?