Question

The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in the manufacturing sector. The hourly wage was $30.67 for Switzerland, $20.20 for Japan, and $23.82 for the U.S. Assume that in all three countries, the standard deviation of hourly labor rates is $3.00.

Appendix A Statistical Tables

a. Suppose 40 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will be between $30.00 and $31.00?
b. Suppose 37 manufacturing workers are selected randomly from across Japan. What is the probability that the sample average will exceed $21.00?
c. Suppose 49 manufacturing workers are selected randomly from across the United States. What is the probability that the sample average will be less than $23.00?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

Answer 1

a) For sample size = 40 > 30, therefore we can apply the Cetral limit theorem here to get the required probability here:

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.6787 is the required probability here.

b) Again using the same method as above, the probability here is computed as:

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0526 is the required probability here.

c) Similar to above part, the probability here is computed as:

Getting it from the standard normal tables, we have here:

Therefore 0.0281 is the required probability here.