Question

Quality control is an important issue at ACME Company which manufactures light bulbs. In order to conduct testing of the life hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6).

378, 361, 350, 375, 200, 391, 375, 368, 321

4. What is the range?
A. 342.43
B. 3424.3
C. 58.5
D. 191
E. 1060

5. What is the variance?
A. 342.43
B. 3424.3
C. 58.5
D. 191
E. 10609

6. What is the standard deviation?
A. 342.43
B. 3424.3
C. 58.5
D. 191
E. 10609

Answer 1

Answer: 4. D. 191

5. B. 3424.3

6. C. 58.5

Explanation:

Given : ACME Company randomly sampled nine light bulbs and measured how many hours they lasted .

378, 361, 350, 375, 200, 391, 375, 368, 321

sample size : n=9

4. Range = Maximum value - Minimum value

= 391-200= 191

∴Range = 191

5 . Let x denotes the data values.

Mean
`\overline{x}=346.6`

x
`(x_i-\overline{x})`
`(x_i-\overline{x})^2`

378 31.4 985.96

361 14.4 207.36

350 3.4 11.56

375 28.4 806.56

200 - 146.6 21491.56

391 44.4 1971.36

375 28.4 806.56

368 21.4 457.96

321 -25.6 655.36

`\sum(x_i-\overline{x})^2=27394.24`

Variance =
`=\frac{\sum(x_i-\overline{x})^2}{n-1}`

`=(27394.24)/(8)=3424.28\approx3424.3`

∴ Variance =3424.3

5. Standard deviation =
`\dsqrt{Variance}=√(3424.28)=58.5173478551\approx58.5`

∴ Standard deviation =58.5