Question

The mean life of a television set is 109 months with a variance of 324. If a sample of 77 televisions is randomly selected, what is the probability that the sample mean would be less than 110.2 months? Round your answer to four decimal places.

Answer 1

To find the probability that the sample mean would be less than 110.2 months, we need to calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that the sample mean would be less than 110.2 months, we need to calculate the z-score and use the standard normal distribution table.

First, let's calculate the z-score using the formula:

z = (sample mean - population mean) / (standard deviation / √n)

In this case, the population mean is 109 months, the standard deviation is √324 months, and the sample size is 77. Plugging in these values:

z = (110.2 - 109) / (√324 / √77) ≈ 1.002

Next, we can use the standard normal distribution table or a calculator to find the probability corresponding to the z-score 1.002. The probability is approximately 0.8434.