A survey of 100 online shoppers at a certain popular web-store reveals the following probability distribution of the number of items purchased per hit.

x= 0 1 2 3 4 5 6 7 8

p(x)= .32 .23 .24 .09 .05 .04 .02 jQuery22409089459649222869_1590041223592? .01

1) Assuming that p(x) is the true probability distribution function, what is the probability that the next customer who visits the website will purchase between 2 and 5 (inclusive) items.

2) Assuming that p(x) is a valid probability distribution, find p(7).

3) Calculate the expected number of items purchased per hit.

4) Calculate the standard deviation of the number of items purchased per hit.

5) What is the probability that a customer will complete the transaction (purchase at least one item) during a hit?