SOLUTION: The bank officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the

Click here to see ALL problems on Probability-and-statistics

Question 204297: The bank officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The bank officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260?
-------------------------
Find the z-value of 230 and of 260:
z(230) = (230-240)/(60/sqrt(36)] = 60/60 = 1
---
z(260) = (260-240)/(60/sqrt(36)) = 20/[60/6) = 2
--------------------------------
P(230 < x < 260) = P(1 < z < 2) = 0.1359...
---------------------------------
Cheers,
Stan H.