Final answer:
To find the probability that the mean of a sample of 60 computers would differ from the population mean by less than 2.94 months, we use the central limit theorem. The probability is approximately 0.9978.
Step-by-step explanation:
To find the probability that the mean of a sample of 60 computers would differ from the population mean by less than 2.94 months, we need to use the central limit theorem. According to the central limit theorem, the distribution of sample means approaches a normal distribution as the sample size increases.
First, we calculate the standard deviation of the sample mean using the formula: standard deviation = population standard deviation / sqrt(sample size). In this case, the population standard deviation is the square root of the variance, which is 8.
The standard deviation of the sample mean is 8 / sqrt(60) = 1.0328 months. Next, we calculate the z-score corresponding to a difference of 2.94 months using the formula: z = (sample mean - population mean) / standard deviation.
The z-score is (2.94 - 0) / 1.0328 = 2.847. Finally, we use a standard normal distribution table or a calculator to find the probability that a z-score is less than 2.847. The probability is approximately 0.9978, rounded to four decimal places.