what is the proability that a random sample of 17 pregnancie

what is the proability that a random sample of 17 pregnancies has a mean gestation period of 193 days or less? The probability that the mean of a random sample of 17 pregnancies is less than 193 days is approximately ? round to four decimal places as needed.

Solution

Standard error =sd/sqrt(n) = 10/sqrt(17) =2.4254

z value for 193=(193-197)/2.4254 = -1.65

P( MEAN x<193) =p(Z < -1.65)= 0.0495

probability that the mean of a random sample of 17 pregnancies is less than 193 days is 0.0495