Final answer:
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.