I need help with (c) portion of the question.. nita or 2-2 MyStatLab: Module Two

Question

I need help with (c) portion of the question..

nita or 2-2 MyStatLab: Module Two Problem Set Suppose the lenghe of the pregiascies of a certain aninal ave apporoximately normaly disributed with mem u- 123 day and stanard deviation" ti days. (a) What is the probability that a randomly selected p peegeancy lasts less than 119 days? erobabliky thet a randomly selected pregnascy lasts less than 19 days is approdimaely 0,3594. (Roued to fue decimal places as needed.) b) What is the probebiy that a random sample of 15 pregnancies has a mean gestation peniod of 119 days or less? The probabãity that the mean of a a randoen sangle of 1S pregmancies is less than 119 days is approsimately 0.0795 Round to four decimal places as needed) ic) What is the yeobability that a random sample of 38 gregnarljes has a roean gestation geriod of 119 days or less? The probabity that the mean ofa arandam sample of 38 pregnane ests less than 119 days s appro naelyDand to Esur decimal places as needed.)

Explanation / Answer

Mean ( u ) =123
Standard Deviation ( sd )=11
Number ( n ) = 38
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 119) = (119-123)/11/ Sqrt ( 38 )
= -4/1.784= -2.2416
= P ( Z >-2.2416) From Standard Normal Table
= 0.9875                  
P(X < = 119) = (1 - P(X > 119)
= 1 - 0.9875 = 0.0125                  

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