Question: 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.

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?

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