Economics and Finance
Bank overdraft fees range from $10 to $38, consumers believe they are annoying and excessive, and these fees are a huge revenue source for banks. The Overdraft Protection Act of 2013 is designed to limit overdraft fees in a variety of ways and to require fees to be reasonable and proportional to the amount of the overdraft. Let X be the amount of an overdraft fee for a randomly selected bank. The probability distribution for X is given in the table below.
|
X
|
10
|
12
|
15
|
20
|
25
|
27
|
30
|
35
|
38
|
|
P( x)
|
0.02
|
0.06
|
0.08
|
0.10
|
0.16
|
0.28
|
0.15
|
0.07
|
0.08
|
a. Find the mean, variance, and standard deviation of the overdraft amount.
b. Find the probability that a randomly selected bank has an overdraft fee greater than $25.
c. Find the probability that a randomly selected bank has an overdraft fee less than m 2 s.
d. Suppose three banks are selected at random. What is the probability that at least one bank has an overdraft fee less than $20?