Suppose the lengths of the pregnancies of a certain animal a

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu = 173 days and standard deviation sigma = 15 days. Complete parts (a) through (c). What is the probability that a randomly selected pregnancy lasts less than 168 days? The probability that a randomly selected pregnancy lasts less than 168 days is approximately . (Round to four decimal places as needed.) What is the probability that a random sample of 14 pregnancies has a mean gestation period of less than 168 days? The probability that the mean of a random sample of 14 pregnancies is less than 168 days is approximately . (Round to four decimal places as needed.) What is the probability that a random sample of 53 pregnancies has a mean gestation period of less than 168 days? The probability that the mean of a random sample of 53 pregnancies is less than 168 days is approximately . (Round to four decimal places as needed.)

Solution

Normal Distribution
Mean ( u ) =173
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 168) = (168-173)/15
= -5/15= -0.3333
= P ( Z <-0.3333) From Standard Normal Table
= 0.3694                  
b)
P(X < 168) = (168-173)/15/ Sqrt ( 14 )
= -5/4.0089= -1.2472
= P ( Z <-1.2472) From Standard NOrmal Table
= 0.1062                  
c)
P(X < 168) = (168-173)/15/ Sqrt ( 53 )
= -5/2.0604= -2.4267
= P ( Z <-2.4267) From Standard NOrmal Table
= 0.0076