Question

A firm wants to establish how long it is supposed to take to assemble a certain product. A random sample of 13 employees is selected and the company measures how long it takes each of them to assemble the product rounded to the nearest minute.

Data: 5; 45; 11; 9; 14; 22; 45; 16; 30; 25; 19; 45; 15

Solve the following by hand.

You must show your work including the formulas and all your computations.

10. The variance is: ______

11. The standard deviation is: ______

12. The coefficient of variation is: ______

13. Convert the 8 into a Z-score: _______

14. Convert the 30 into a Z-Score _______

Answer 1

Sample size, n =13

Sample mean, =(5+45+......+15)/13 =301/13 =23.1538

10.

The variance, s² = =(5 - 23.1538)² + (45 - 23.1538)² +......... + (15 - 23.1538)²/(13 - 1) =198.3077

11.

The standard deviation, s = = =14.0822

12.

The coefficient of variation, CV =(s/)*100 =(14.0822/23.1538)*100 =60.82%

13.

Convert the 8 into a Z-score:

X =8

Z =(X - ​​​​​​)/s =(8 - 23.1538)/14.0822 = -1.0761

14.

Convert the 30 into a Z-Score:

X =30

Z =(X - ​​​​​​)/s =(30 - 23.1538)/14.0822 =0.4862