The owner of a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer.
x 1 2 3 4 5 6 7 8 9 10
P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01
a. What is the mean the number of oranges purchased?
b. What is the standard deviation for the number of oranges purchased?