A large shipment of Granny Smith apples arrives at a grocery store. Weights of the apples are known to follow a normal distribution with mean 152 grams and standard deviation 16 grams.

Question

A large shipment of Granny Smith apples arrives at a grocery store.  Weights of the apples are known to follow a normal distribution with mean 152 grams and standard deviation 16 grams.

anonymous · Answer

That is X~N(152,16^2)
Then?

anonymous · Answer

(a)  We take a random sample of three of the waiter's customers.  Can you calculate the probability that the mean tip for these customers is less than $9.43?

(b) If we take a random sample of 35 of the waiter's customers, what is the probability that the mean tip for these customers is greater than $6.13?    

(c)  If we take a random sample of 45 of the waiter's customers, what is the probability that the mean tip for these customers is between $5.08 and $6.87?

anonymous · Answer

(a) np = mean
If either or both np and nq are less than 5, a binomial distribution is to be used. Otherwise, a normal distribution is to be used.
q=1-p
p=mean/n
Can you carry on from here?