Answer:
AI-generated answer
To solve this problem, we can use the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean.
The CLT states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. In this case, the sample size is 72, which is considered large.
The mean of the sampling distribution of the sample mean is equal to the population mean, which is 105 months.
The standard deviation of the sampling distribution of the sample mean, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size:
Standard Error = Population Standard Deviation / √Sample Size
Standard Error = 9 / √72
To find the probability that the mean of a sample of 72 computers would differ from the population mean by less than 0.32 months, we need to standardize this difference using the standard error.
Z = (X - μ) / SE
Z = (0.32 - 0) / (9 / √72)
By calculating this Z-score, we can then look up the corresponding area under the standard normal distribution curve using a Z-table or a calculator.
Finally, we can find the probability by subtracting the area obtained from 0.5, as we are interested in the area under the curve to the left of the given Z-score.
I hope this explanation helps! Let me know if you have any further questions.
Explanation: