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 $4.00.

a. Suppose 37 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 48 manufacturing workers are selected randomly from across the United States. What is the probability that the sample average will be less than $22.85?

Answer 1

Answer:(a)

Here, μ = 30.67, σ = 4/sqrt(37) = 0.658, x1 = 30 and x2 = 31.

z = (x - μ)/σ
z1 = (30 - 30.67)/0.658 = -1.018
z2 = (31 - 30.67)/0.658 = 0.502

since probability that the sample average will be between $30.00 and $31.00

= P(-1.018<= z <= 0.502)

= 0.5378

Answer:(b)

Here, μ = 20.20, σ = 4/sqrt(35) = 0.6761

z = (21 - 20.20)/0.6761 =1.1833

probability that the sample average will exceed $21.00

=P(Z>= 1.1833)

= 0.1183

Answer:(c)

Here, μ = 23.82, σ = 4/sqrt(48) = 0.5774

z = (22.85 - 23.82)/0.5774 = -1.6799

probability that the sample average will be less than $22.85

=P(Z<=-1.6799)

=0.0465