Question

A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 75 months with a standard deviation of 5 months. If the claim is true, what is the probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors

Answer 1

To find the probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors, calculate the z-score and use a standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that the mean monitor life would be greater than 74.4 months in a sample of 85 monitors, we can use the standard normal distribution. With a mean of 75 months and a standard deviation of 5 months, we calculate the z-score:

z = (x - μ) / (σ / √n)

where:

x = sample mean

μ = population mean

σ = population standard deviation

n = sample size

In this case, x = 74.4 months, μ = 75 months, σ = 5 months, and n = 85 monitors:

z = (74.4 - 75) / (5 / √85)

Calculating this value, we can then find the probability of z being greater than that value using a standard normal distribution table or a calculator.

Based on the value of z, we can determine the probability of the mean monitor life being greater than 74.4 months in a sample of 85 monitors.