Need help finding the probability

Question

"Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 14 minutes. Consider 49 of the races"

1. Let X = the average of the 49 races.

I need help finding the probability that the average of the sample will be between 142 and 145 minutes in these 49 marathons (answer must be rounded to four decimal places)

Can someone walk me through this step by step? it would really help

Answer 1

x = N(143,14)

z = (x - mean)/standard error converts to N(0,1)

mean = 143, standard error = SD/square root sample size = 14/7 = 2

z = (x - 143)/2

P(142 < x < 145) = P((142-143)/2 < z < (145-143)/2) = P(-0.5 < z < 1) = P(z < 1) - P(z < -0.5) = 0.8413 - 0.3085 = 0.5328