question1

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of n=75, find the probability of a sample mean being greater than 223 if=222 and =6.1

question 2

The population mean and standard deviation are given below. Find the indicated probability and determine whether the given sample mean would be considered unusual.

For a sample of n=36, find the probability of a sample mean being less than 12,751 or greater than 12,754 when =12,751 and =1.4.

Question 3

Find the indicated probability and interpret the result.

From 1975 through 2020, the mean annual gain of the Dow Jones Industrial Average was

651. A random sample of 32 years is selected from this population. What is the probability that the mean gain for the sample was between

500 and 800? Assume =1541.

Question 4

The lengths of lumber a machine cuts are normally distributed with a mean of 101 inches and a standard deviation of 0.6 inch.

(a) What is the probability that a randomly selected board cut by the machine has a length greater than

101.31 inches?

(b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 101.31 inches?