The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $9. Within what range are 68% of her phone bills?

go to

http://davidmlane.com/hyperstat/z_table.html

first click on "value from an area"
enter 0.69 into "area"
enter 55 as the mean
enter 9 as the sd

click on "between" to get:

$45.86 and $64.147

To find the range within which 68% of Jen's phone bills fall, we need to calculate the range that covers one standard deviation on both sides of the mean.

Step 1: Calculate one standard deviation.
The mean is $55, and the standard deviation is $9. We want to find the range within one standard deviation of the mean.
One standard deviation is calculated as Mean ± Standard Deviation.
So, one standard deviation is $55 ± $9.

Step 2: Calculate the lower end of the range.
The lower end of the range is the mean minus one standard deviation.
Lower end of the range = $55 - $9 = $46.

Step 3: Calculate the upper end of the range.
The upper end of the range is the mean plus one standard deviation.
Upper end of the range = $55 + $9 = $64.

Therefore, 68% of Jen's phone bills fall within the range of $46 to $64.

To find the range within which 68% of Jen's phone bills fall, we can use the concept of the empirical rule, also known as the 68-95-99.7 rule, which applies to data that follows a normal distribution. According to this rule:

- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.

In this case, we know that the mean of Jen's phone bill is $55, and the standard deviation is $9. Therefore, we can calculate the range within which 68% of her phone bills fall as follows:

1. Find the lower limit: Subtract one standard deviation ($9) from the mean ($55 - $9 = $46).
2. Find the upper limit: Add one standard deviation ($9) to the mean ($55 + $9 = $64).

Therefore, approximately 68% of Jen's phone bills will be within the range of $46 to $64.

Use the empirical rule to solve the problem.

1) The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of
$12.
a) Write in the cutoffs and percentages for the phone bill.
b) What percentage of her phone bills are between $19 and $91?
c) What percentage of her phone bills are less than $67?
d) What percentage of her phone bills are greater than $79?
e) What is the median?
2