Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 108 hours. A random sample of 64 light bulbs indicated a sample mean life of 410 hours. Complete parts​ (a) through​ (d) below.

a. Construct a 95​% confidence interval estimate for the population mean life of light bulbs in this shipment.

The 95​% confidence interval estimate is from a lower limit of ___ hours to an upper limit of ___ hours.

Answer 1

Solution :

Given that,

= 410

= 108

n = 64

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (108 / 64)

= 26.4600

At 95% confidence interval estimate of the population mean is,

- E < < + E

410 - 26.4600 < < 410 - 26.4600

383.5400< < 436.4600

(383.5400 ,  436.4600)

lower limit of 385.5400  hours to an upper limit of 436.4600