Both are normally distributed. For the net sales, the mean is 180 million and the standard deviation is 25 million. For the number of employees the mean is 1,500 and the standard deviation is 120. Clarion Fabricators had sales of 170 million and 1,850 employees.
A: Convert Clarions sales and number of employees to z- values?
B: Compare Clarions employees and number of employees with those of the other fabricators: percent they have more employees than Clarions? Percent the aluminum fabricators have greater net sales than Clarions?
A: Z = (score-mean)/SD
B: No data on other fabricators.
To convert Clarion's sales and number of employees to z-values, we need to use the formulas for standardizing a normal distribution:
Z-score for sales = (Clarion's sales - Mean sales) / Standard deviation of sales
Z-score for employees = (Clarion's number of employees - Mean number of employees) / Standard deviation of number of employees
A:
Given values:
Clarion's sales = 170 million
Mean sales = 180 million
Standard deviation of sales = 25 million
To calculate the z-score for sales:
Z-score for sales = (170 - 180) / 25
Z-score for sales = -10 / 25
Z-score for sales = -0.4
Clarion's z-score for sales is -0.4.
Given values:
Clarion's number of employees = 1850
Mean number of employees = 1500
Standard deviation of number of employees = 120
To calculate the z-score for employees:
Z-score for employees = (1850 - 1500) / 120
Z-score for employees = 350 / 120
Z-score for employees ≈ 2.917
Clarion's z-score for employees is approximately 2.917.
B:
To compare Clarion's number of employees with other fabricators, we need to calculate the percentage of fabricators that have more employees than Clarion. This can be done by finding the area under the standard normal curve to the right of Clarion's z-score for employees.
Using a standard normal distribution table or a statistical software:
Percent they have more employees than Clarion ≈ 1 - (cumulative probability value for z-score = 2.917)
Similarly, to compare the net sales of aluminum fabricators with Clarion, we need to calculate the percentage of net sales that are greater than Clarion's sales. This can be done by finding the area under the standard normal curve to the right of Clarion's z-score for sales.
Percent the aluminum fabricators have greater net sales than Clarion ≈ 1 - (cumulative probability value for z-score = -0.4)
Both of these percentage calculations can be obtained from a standard normal distribution table or by using statistical software.