Question

In: Statistics and Probability

The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...

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 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 34 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 $22.75?

Solutions

Expert Solution

a)

µ = 30.67, σ = 4, n = 42

P(30 < X̅ < 31) =

= P( (30-30.67)/(4/√42) < (X-µ)/(σ/√n) < (31-30.67)/(4/√42) )

= P(-1.0855 < z < 0.5347)

= P(z < 0.5347) - P(z < -1.0855)

Using excel function:

= NORM.S.DIST(0.5347, 1) - NORM.S.DIST(-1.0855, 1)

= 0.5647

b)

µ = 20.2, σ = 4, n = 34

P(X̅ > 21) =

= P( (X̅-μ)/(σ/√n) > (21-20.2)/(4/√34) )

= P(z > 1.1662)

= 1 - P(z < 1.1662)

Using excel function:

= 1 - NORM.S.DIST(1.1662, 1)

= 0.1218

c)

µ = 23.82, σ = 4, n = 49

P(X̅ < 22.75) =

= P( (X̅-μ)/(σ/√n) < (22.75-23.82)/(4/√49) )

= P(z < -1.8725)

Using excel function:

= NORM.S.DIST(-1.8725, 1)

= 0.0306


Related Solutions

The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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. Appendix A Statistical Tables a. Suppose 35 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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 38 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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. a. Suppose 36 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...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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. 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...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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 35 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.) a. b. c. a. Suppose 43 manufacturing workers are selected randomly from across Switzerland and...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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 35 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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...
The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in...
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 44 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT