The weight of cherries in a pie, X, has the following discrete probability ...

The weight of cherries in a pie, X, has the following discrete probability distribution:
 

 x           4       5      6      7
P(X=x)   10%  30% 40%  20%
 

a) find the mean, st. dev, and variance
 

b) If you took samples of the weight of cherries in 25 cherry pies, what mean and standard deviation would you expect to find from the weights of all cherries in the pies?
 

c) Find the probability that the average number of cherries in 25 pies will be less than 5.4 lbs. assuming that the distribution is roughly normal.