A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P(

Question

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P(  < 51.5).
A).9641 
B).0359 
C).1389 
D).9999

Quizplus · Accepted Answer

Using the central limit theorem, we know that the sample mean follows a normal distribution with mean=50 and standard deviation=5/sqrt(36)=5/6.
Therefore, z=(51.5-50)/(5/6)=1.8
Using a standard normal distribution table, we find that P(Z<1.8)=0.9641.
Thus, P( 11eb06d7_55f6_4401_8177_e361c4b7e34c_TB1736_11 < 51.5)=0.9641.

A Random Sample of Size 36 Is Taken from a Population