The lifespan in hours of a 60watt light bulb is a random var

The lifespan (in hours) of a 60-watt light bulb is a random variable that has a normal distribution with standard deviation = 30. A random sample of 25 bulbs put on test produced a sample mean lifespan of = 1038. Based on the above information, the 92% confidence interval estimate for the mean lifespan, , of a 60-watt light bulb is

Solution

using Z distribution because we know the standard deviation of population ( sigma)

alpha = 1 - 0.92 = 0.08

alpha / 2 = 0.04

Z = 1.75

I : xbar +/- Z * sigma / srqt (n)

I : 1038 +/- 1.75 * 30 / srqt(25)

I: 1038 +/- 10.5

I: [ 1027.5 < miu < 1048.5 }