The net sales and the number of employees for aluminum fabricators with similar

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 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 (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.) (b) Interpret the z values obtained in Req (a) (Round your answers to 2 decimal places.) Net sales are ________ standard deviations the mean. Employee is _______ standard deviations the mean. (c) Compare Clarion's sales and number of employees with those of the other fabricators (Round your answers to 2 decimal places.) ________ % of the aluminum fabricators have greater net sales compared with Clarion Only ________ % have more employees than Clarion

Explanation / Answer

Solution:-

(a) Given, for net sales mean = $180 million

and standard deviation = $25 million

Calculating z value for net sale,

z = x – / ,

= (180 - 170) / 25 = 0.4

For employees, mean = 1500

and Standard deviation = 120

z = x – / ,

= (1500 - 1850) / 150 = -2.33

(b) Interpreting z value

Net sales are 0.4 (34.46%) standard deviations above the mean.

Employees is -2.33 (.98%) standard deviations below the mean.

(c) 34.46% of aluminium fabricators have greater net sales compared with Clarion.

0.98% have more employees than Clarion.

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