Question

An electrical firm manufacturers light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 48 hours. If a sample of 36 bulbs has an average life of 780 hours, find the bounds of a 99% confidence interval for the population mean of all bulbs produced by this firm.

780\pm3.29\cdot(8)

None of these

Answer 1

solution:

the length of life of bulb is approximately normally distributed with standard deviation hours.

a sample of n = 36 has a mean of hours

we need to find a 99% confidence interval for mean life of all bulb

confidence level = 99% = 0.99

since population standard deviation is known, so confidence interval would be

where is the z value having an area to the right

= = 2.575

so lower bound = 780 - 20.6 = 759.4

upper bound = 780 + 20.6 = 800.6

so 99% confidence interval for the mean life of all bulb would be (759.4, 800.6)