SOLUTION: 9. A normal distribution of utility bills shows the mean to be $100 and the standard deviation of $12. a) What percent of the utility bills are more than $125. b) If 300 utilit

Question 1120406: 9. A normal distribution of utility bills shows the mean to be $100 and the standard deviation of $12.
a) What percent of the utility bills are more than $125.
b) If 300 utility bills are randomly selected, about how many of them would you expect to be less than $90?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) Probability (P) ( X > 125 ) = 1 - P ( X < 125 )
:
z-score(125) = (125 - 100)/12 = 2.0833
:
using table of z-scores, the probability associated with 2.0833 is 0.9812
:
(P) ( X > 125 ) = 1 - 0.9812 = 0.0188
:
b) because we know the standard deviation of the population, we can use the normal distribution in our calculations
:
z-score(90) = ( 90 - 100 ) / 12 = −0.8333
:
P ( X < 90 ) = 0.2033
:
300 * 0.2033 = 60.99 approximately 61
:

RELATED QUESTIONS
9. A normal distribution of utility bills shows the mean to be $100 and the standard... (answered by Boreal)

Monthly utility bills in a certain city are normally distributed with a mean of 100 and a (answered by stanbon)

A national achievement test has a normal distribution, a mean of 1000, and a standard... (answered by Fombitz)

for a normal distribution with a mean of 20 and standard deviation of 5, what percent of... (answered by swincher4391)

The retail price of 12-pack soda can be characterized as having a normal distribution... (answered by Boreal)

IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. (answered by stanbon)

If X has a normal distribution with mean 80 and standard deviation 12, what is the... (answered by stanbon)

For a normal distribution with mean of 100 and a standard deviation of 12, find the... (answered by rothauserc)

In a normal distribution with a mean of 70 and a standard deviation of 3, what percent of (answered by tommyt3rd)