Question

The life of a PH computer is normally distributed with mean 3 years with standard deviation 1.7 years. Your business buys 36 PH computers. What is the probability that the average life span of those 36 computers will be less than 2.9 years?

Answer 1

Let X be the random variable that denotes the life of a PH computer.

Given, X Normal ( = 3,² = 1.7²)

Your business buys 36 PH computers. Therefore, n = 36

According to the central limit theorem, if the population distribution is normally distributed with mean and variance ², then the distribution of the sample mean is normally distributed with mean and variance ²/n, where n is the sample size.

Using the central limit theorem, Normal ( = 3, ²/n = 1.7²/36)

P( < 2.9) = P(Z < (2.9 - 3) / (1.7 / ))

                   = P(Z < -0.35)

                   = P(Z > 0.35)     .............( P(Z < -a) = P(Z > a))

                   = 1 - P(Z < 0.35)

                   = 1 - 0.63683     .............(value from standard normal table)

                   = 0.36317

Therefore, the probability that the average life span of those 36 computers will be less than 2.9 years is 0.3632