Given that the population mean (μ) is 121 months, the sample mean (x̄) can vary by less than 2.2 months.
The standard error of the mean (SE) can be calculated using the formula:
SE = sqrt(variance / sample size) = sqrt(256 / 95) = sqrt(2.6842) ≈ 1.6395
Now, we can calculate the z-score for a difference of 2.2 months:
z = (2.2 - 0) / 1.6395 = 1.3419
Using the z-table or calculator, the probability corresponding to a z-score of 1.3419 is approximately 0.9099.
Therefore, the probability that the sample mean would differ from the true mean by less than 2.2 months is approximately 0.9099.
The mean life of a television set is 121
months with a variance of 256
.
If a sample of 95
televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 2.2
months? Round your answer to four decimal places.
1 answer