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 42 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 35 manufacturing workers are selected randomly from across Japan. What is the probability that the sample average will exceed $21.00?

c. Suppose 50 manufacturing workers are selected randomly from across the United States. What is the probability that the sample average will be less than $22.80

Answer 1

solution:

switzerland mean wage rate = ,

Japan mean wage rate =

U.S. mean wage rate=

a) for switzerland n = 42

P(30 < X < 31)

for X = 30 ,

for X = 31 ,

P(30 < X < 31) = (value of z to the left of 0.71) - (value of z to the left of -1.45)

P(30 < X < 31) = 0.7611 - 0.0735 = 0.6876

b) for Japan n = 35

P(X > 21)

for X = 21,

P(X > 21) = 1 value of z to the left of 1.58

P(X > 21) = 1 - 0.9429 = 0.0571

c) for U.S. n = 50

P(X < 22.80)

P(X < 22.80) = value of z to the left of -2.4

P(X < 22.80) = 0.0082