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

Distribution of population x is unknown but here sample size 50 which is greater than 30 using CLT sample mean is normally distributed.

Here n > 30 so we assume sample is normally distributed.

Question. 2

X = 61500

They asked to find probability for mean less than 61500. Do standard deviation for mean

Answer :

Probability is less than 61500 is 0.0033

Stat crunch output:

Stat crunch instructions:

Go to Stat then choose calculator then normal new window will pop up then plug mean value standard deviation for sample mean and x value then calculate to get probability.

Ti-84/83 instructions

Press 2nd then VARS then normalcdf

Lower = -9999

Upper = 61500

Plug mean and sd then calculate .

Question. 4

Probability is 0.0033 which is below 0.05 so it is unusual.

Ti-84 output: