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 41 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 32 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 $22.75?d. Suppose 48 manufacturing workers are selected randomly from across the United States. What is the probability that the sample average will be less than $22.90?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	30.67
std deviation   =σ=	3.000
sample size       =n=	41

probability =

P(30<X<31)

=

P(-1.43<Z<0.7)=

0.758-0.0764=

0.6816

b)

here mean=       μ=	20.2
std deviation   =σ=	3
sample size       =n=	32
std error=σx̅=σ/√n=	0.5303

probability =

P(X>21)

=

P(Z>1.51)=

1-P(Z<1.51)=

1-0.9345=

0.0655

c)

probability =

P(X<22.75)

=

P(Z<-2.45)=

0.0071

d)

probability =

P(X<22.9)

=

P(Z<-2.12)=

0.0170