Find probability

Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 13 minutes. Consider 49 of the races.

Let X

 = the average of the 49 races.

Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)

Answer 1

Distribution of sample means will be normal, with mean 145 with standard deviation 13 / sqrt (49) = 13 / 7

Pr (sample mean is between 144 and 148) = area under normal distribution between X = 144 and 148 with above parameters

On a TI-84 this will be normalcdf (144, 148, 145, 13/7) = 0.6518 to 4 decimal places