Suppose that the probability that a drive-thru fills an order correctly is 0.65. A random sample of 22 independent drive-thru orders is taken. You are interested in the number of drive-thru orders in...

Suppose that the probability that a drive-thru fills an order correctly is 0.65. A random sample of 22 independent drive-thru orders is taken. You are interested in the number of drive-thru orders in the sample that are filled correctly.

a. In words, define the random Variable X. What kind of distribution does X have and what are its parameters, specific to this problem?

b. Find the probability that exactly 11 orders are filled correctly.

c. Find the probability that at most 11 orders are filled correctly.

d. Find the probability that at least 11 orders are filled correctly.

e. Find the probability that less than 11 orders are filled correctly.

f. Find the probability that more than 11 orders are filled correctly.

g. Find the mean and standard deviation of X.

h. Find the probability that X is within 1 standard deviation of its mean.