Anormally distributed population has a mean of 475 and a standard deviation of 60.
a. determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 435.
b. determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 501.

a. 0.0038    b. 0.0151

Step-by-step explanation:

Given : A normally distributed population has a mean of 475 and a standard deviation of 60.

i.e.  

Let be the sample mean.

Formula :

a. For sample n= 16

Then, the probability that a random sample of size 16 selected from this population will have a sample mean less than 435. will be :-

∴ The probability that a random sample of size 16 selected from this population will have a sample mean less than 435 = 0.0038

b. For sample n= 25

Then, the probability that a random sample of size 16 selected from this population will have a sample mean less than 435. will be :-

∴ The probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 501 = 0.0418