According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.

a. What is the probability that a randomly selected monthly cell phone bill is more than $100?
b. What is the probability that a randomly selected monthly cell phone bill is between $60 and $83?
c. What is the probability that a randomly selected monthly cell phone bill is between $80 and $90?
d. What is the probability that a randomly selected monthly cell phone bill is no more than $55?

a)

And we can find this probability using the complement rule:

b)

And we can find this probability with this difference:

c)

And we can find this probability with this difference:

d)

And we can find this probability using the normal standard table:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the average monthly household cellular phone bill of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule:

Part b

And we can find this probability with this difference:

Part c

And we can find this probability with this difference:

Part d

And we can find this probability using the normal standard table:

sine

step-by-step explanation: