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.

1. Convert Clarion's sales and number of employees to z values. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

Net sales _____

Employees _______

2. Interpret the z values obtained in part a. (Round your answers to 2 decimal places.)

Net sales are _____ standard deviations _________ the mean

employees are ______ standard deviations _______ the mean

3. 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.

Answer 1

Solution:-

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

and standard deviation = $25 million

Calculating z value for net sale,

z = x – μ / σ,

= (180 - 170) / 25 = 0.4

For employees, mean = 1500

and Standard deviation = 120

z = x – μ / σ,

= (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.