In: Statistics and Probability
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 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 38 manufacturing workers are selected
randomly from across Japan. What is the probability that the sample
average will exceed $21.00?
c. Suppose 47 manufacturing workers are selected
randomly from across the United States. What is the probability
that the sample average will be less than $22.90?
Using central limit theorem,
P( < x) = P(Z < (x - ) / ( / sqrt(n) ))
a)
P(30 < < 31) = P( < 31) - P( < 30)
= P(Z < (31 - 30.67) / (3 / sqrt(37) ) ) - P(Z < (30 - 30.67) / (3 / sqrt(37) ) )
= P(Z < 0.67) - P( Z < -1.83)
= 0.7486 - 0.0336
= 0.7150
b)
P( > 21) = P(Z > (21 - 20.20) / (3 / sqrt(38) ) )
= P(Z > 1.64)
= 0.0505
c)
P( < 22.90) = P(Z < (22.90 - 23.82) / (3 / sqrt(47) ) )
= P(Z< -2.10)
= 0.0179