the amount of jens month phone bill is normally distributed with a mean of $69 and a standard deviation of $10. what is 68.26% of phone bill between?

I just love this applet for this work, replaces all those nasty charts and tables in the back of text-books

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

click on "value from an area"
enter mean as 69
SD as 10
click on "between" to get
$59 and $79

To find the range within which 68.26% of the phone bill falls, we can use the properties of the normal distribution and the given mean and standard deviation.

First, let's understand the properties of the normal distribution. In a normal distribution curve, roughly 68.26% of the data falls within one standard deviation of the mean. This means that we need to find the range within one standard deviation below and above the mean of the phone bill.

Given:
Mean (μ) = $69
Standard Deviation (σ) = $10

To find the range of 68.26% of the phone bill, we can compute the lower and upper bounds as follows:

Lower Bound = Mean - 1 standard deviation
= 69 - 10
= $59

Upper Bound = Mean + 1 standard deviation
= 69 + 10
= $79

Hence, 68.26% of the phone bill is expected to fall within the range of $59 and $79.

To find the range that encompasses 68.26% of the phone bill amounts, we will use the properties of the normal distribution.

Step 1: Find the standard deviation from the mean.
Since the standard deviation is 10, we know that 1 standard deviation (1σ) in either direction from the mean will capture approximately 68.26% of the data.

Step 2: Calculate the lower boundary.
To find the lower boundary, subtract 1 standard deviation from the mean.
Lower boundary = 69 - 10 = 59

Step 3: Calculate the upper boundary.
To find the upper boundary, add 1 standard deviation to the mean.
Upper boundary = 69 + 10 = 79

Therefore, approximately 68.26% of the phone bill amounts are between $59 and $79.