Question

Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.1 ounces and a standard deviation of 1.1 ounces.

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.6 ounces. Round your answer to 4 decimal places.


(b) If 8 potatoes are randomly selected, find the probability that the mean weight is more than 8.7 ounces. Round your answer to 4 decimal places.

Answer 1

Solution: Given that mean = 8.1, sd = 1.1

(a) for n = 5
P(X < 9.6) = P((X-mean)/(sd/sqrt(5)) < (9.6-8.1)/(1.1/sqrt(5)))
= P(Z < 3.0492)
= 0.9989

=> Use the standard normal table to find this area :

(b) for n = 8
P( X > 8.7) = P(Z > (8.7-8.1)/(1.1/sqrt(8)))
= P(Z > 1.5428)
= 0.0618

=> Use the standard normal table to find the area below 1.5428 :