Question

The population mean annual salary for high school teachers is $64,500 and the standard deviation is $7,800. A random sample of 50 teachers is obtained from this population.

1. is this sample normally distributed? why or why not?

2. What is the probability that the mean salary is less than $61,500?

3.Write the entire STATCrunch or calculator instructions/commands you use to solve this problem. Use the appropriate probability statement (ex. ?(? ≤ 2) = .20) when expressing your answer.

4.Is the probability that the mean salary is less than $61,500 an unusual event? Explain your reasoning.

Answer 1

1:

Sample can be normally distributed becuase sample size is large. The shape of sample data is depend on population distribution. It is not given that population is normally distributed so we cannot safely assume that sample is normally distributed.

Since sample size is greater than 30 so we can safely assume that sampling distribution of sample mean will be normally distributed.

2:

3:

Followig is the screen shot of calculator:

4:

Yes becuase above probability is less than 0.05.