The mean lifetime of a tire is 46 months with a variance of 49. if 133 tires are sample, what is the probability that the mean of the sample would differ from the population mean by less than 1.05 months? round your answer to four decimal places.

The correct probabilities is about 0.1192.

To start we need to find the standard deviation, it is the square root of the variance or 7.

Now, we need to find the z-score of a value that is 1.05 months above the mean.

1.05 / 7 = 0.15 produces a value of 0.5596. Since we are dealing with a range from 0.15 below and above the mean, we have 0.0596 to the right of the mean and the same below the mean.

0.0596 x 2 = 0.1192