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:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

step-by-step explanation:

the shape,the size and the distance