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.

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

*(Round the values of z to 2 decimal places. Round your
answers to 4 decimal places.)*

**a.** enter the probability that the sample average
will be between $30.00 and $31.00 supposing that 37 manufacturing
workers are selected randomly from across Switzerland

**b.** enter the probability that the sample average
will exceed $21.00 supposing that 38 manufacturing workers are
selected randomly from across Japan

**c.** enter the probability that the sample average
will be less than $22.80 supposing that 49 manufacturing workers
are selected randomly from across the United States

Answer #1

**Solution:-**

**a) The probability that the sample average will be
between $30.00 and $31.00 is 0.5381.**

n = 37, Mean = 30.67, S.D = 4

x_{1} = 30

x_{2} = 31

By applying normal distribution:-

z_{1} = -1.02

z_{2} = 0.50

P( -1.019 < z < 0.502) = P(z > -1.019) - P(z > 0.502)

P( -1.019 < z < 0.502) = 0.8459 - 0.3078

P( -1.019 < z < 0.502) = 0.5381

**b) The probability that the sample average will exceed
$21.00 is 0.1088.**

n = 38, Mean = 20.20, S.D = 4

x = 21

By applying normal distribution:-

z = 1.23

Use the z-score table or p-value calculator.

**P(z > 1.233) = 0.1088**

**c) The probability that the sample average will be less
than $22.80 is 0.0371.**

n = 49, Mean = 23.82, S.D = 4

x = 22.80

By applying normal distribution:-

z = - 1.79

Use the z-score table or p-value calculator.

**P(z < - 1.785) = 0.0371**

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 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 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...

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...

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 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 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 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 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 be between $30.00 and...

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 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 be between $30.00 and...

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 43 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 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 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...

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