the net sales and the number of employees for aluminum fabricators with similar
ID: 3131685 • Letter: T
Question
the net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. 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 1500 and the standard deviation is 120. clarion fabricators had sales of $170 million and 1850 employees a) convert clarions sales and number of employees to z values b)interpret the z values obtained in part a c) compare clarions sales and number of employees with those of the other fabricators
Explanation / Answer
a)
FOR NET SALES:
As z = (x-u)/sigma, then for x = 170 million, u = 180 million, sigma = 25 million,
z = (170 million - 180 million)/25 million = -0.4 [ANSWER]
FOR NUMBER OF EMPLOYEES:
As z = (x-u)/sigma, then for x = 1850, u = 1500, sigma = 120
z = (1850-1500)/120 = 2.916666667 [ANSWER]
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b)
Hence, Clarion's net sales is 0.4 standard deviations below the mean.
Also, their number of employees is 2.917 standard deviations above the mean.
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c)
As the z score for the net sales is negative, then that means that they are in the lower half of aluminum fabricators in terms of net sales. They have a lower net sales than the majority of companies.
As the z score for the number of employees is positive, then that means that they are in the upper half of aluminum fabricators in terms of net sales. They have more employees than the majority of companies.
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