Question

16. The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

Please show EXCEL work and how it was found, thank you!

Answer 1

Mean of the distribution = $\mu$ = 400 pounds.

Standard deviation = $\sigma$ = 10 pounds

a) P(400 < X < 415) = P(X < 415) - P(X < 400)

The P(X < 415) can be obtained using the formula =NORMDIST(415,400,10,1) in excel and is equal to 0.9332

The P( X < 400) can be obtained using the formula =NORMDIST(400,400,10,1) in excel and is equal to 0.50

So, P(400< X < 415) = 0.9332 - 0.5000 = 0.4332

b) P(395<X<400)

= P(X < 400) - P(X < 395)

= 0.5000 - 0.3085

= 0.1915

P(X < 395) can be obtained using the formula =NORMDIST(395,400,10,1) in Excel and is equal to 0.3085

c) P(X < 395) = 0.3085

(as obtained above).