Question

The mean life of a television set is 115 months with a standard deviation of 16 months. if a sample of 79 televisions is randomly selected, what is the probability that the sample mean would be less than 112.3 months? round your answer to four decimal places.

Answer 1

To answer this question, we need to use the Central Limit Theorem which states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution. We can use the given mean, standard deviation, and sample size to calculate the z-score and then find the corresponding probability using the standard normal distribution table.

Step-by-step explanation:

To answer this question, we need to use the Central Limit Theorem which states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution. We can use the given mean, standard deviation, and sample size to calculate the z-score and then find the corresponding probability using the standard normal distribution table.

Step 1: Calculate the standard error of the mean (SEM) using the formula SEM = standard deviation/sqrt (sample size).

SEM = 16 / sqrt(79) ≈ 1.7985.

Step 2: Calculate the z-score using the formula z = (sample mean - population mean) / SEM.

z = (112.3 - 115) / 1.7985 ≈ -1.5028.

Step 3: Find the probability using the standard normal distribution table or a calculator. For a z-score of -1.5028, the probability is approximately 0.0668.

Therefore, the probability that the sample mean would be less than 112.3 months is approximately 0.0668 (or 6.68%).