Question

The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours?

a. No.
b. Yes.
c. Maybe.
d. Do not know

Answer 1

b) yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Explanation:

Explanation:-

Given sample size 'n' = 64

Given standard deviation of the Population (σ)=100

Mean of the sample (x⁻) = 350 hours

95% of confidence interval is determined by

`(x^(-) -Z_(0.95) (S.D)/(√(n) ) , x^(-) +Z_(0.95) (S.D)/(√(n) ) )`

(
`(350 -1.96 (100)/(√(64) ) , 350+1.96(100)/(√(64) ) )`

(350-24.5 , 350+24.5)

(325.5 , 374.5)

Conclusion:-

Yes

The manufacturer has the right to state that the light bulbs last on average 400 hours