According to a recent research report, the average monthly household mobile phone bill is $73. Suppose monthly household mobile phone bills are normally distributed with a standard deviation of $11.35.
(a) What is the probability that a randomly selected monthly mobile phone bill is no more than $55?
(b) What is the probability that a randomly selected monthly mobile phone bill is more than $100?
(c) What is the probability that a randomly selected monthly mobile phone bill is between $80 and $90?
(d) What is the probability that the average mobile phone bill of randomly selected sample of 25 bills is between $71 and $80?
Please be sure to include all workings with your answers.