A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean

Step-by-step explanation:

We want to determine a 95% confidence interval for the population mean.

Number of sample, n = 56

Mean, u = 645 hours

Standard deviation, s = 31 hours

For a confidence level of 95%, the corresponding z value is 1.96.

We will apply the formula

Confidence interval

= mean ± z * standard deviation/√n

It becomes

645 ± 1.96 * 31/√56

= 645 ± 1.96 * 4.142

= 645 ± 8.12

The lower end of the confidence interval is 645 - 8.12 = 636.88

The upper end of the confidence interval is 645 + 8.12 = 653.12

Therefore, with 95% confidence interval for the population mean life of fluorescent light bulbs is between 636.88 hours and 653.12 hours