In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.7 and standard deviation 10.1.

To find the desired percentiles of diastolic blood pressures using the given mean and standard deviation, we can use the Normal Distribution on the TI-84 Plus calculator.

Given:

• Mean (\(\mu\)) = 80.7
• Standard Deviation (\(\sigma\)) = 10.1

(a) Finding the 30th Percentile

To find the 30th percentile, use the inverse normal function:

1. Press 2nd then VARS to access the DISTR menu.
2. Select invNorm (which is usually option 3).
3. Input the following parameters:
   • For the area, enter 0.30 (because we want the 30th percentile).
   • For the mean, enter 80.7.
   • For the standard deviation, enter 10.1.

Thus, enter: invNorm(0.30, 80.7, 10.1) and press ENTER.

Calculating this will give you the 30th percentile of the diastolic blood pressures.

(b) Finding the First Quartile (Q1)

The first quartile corresponds to the 25th percentile.

Repeat the inverse normal steps, this time for the 25th percentile:

1. Select invNorm again.
2. Input the following parameters:
   • For the area, enter 0.25 (because we want the first quartile).
   • For the mean, enter 80.7.
   • For the standard deviation, enter 10.1.

So, enter: invNorm(0.25, 80.7, 10.1) and press ENTER.

Results

After performing these calculations:

• For the 30th percentile: Approximately 76.77
• For the first quartile: Approximately 75.09

So, rounding to at least two decimal places, the answers are:

(a) 76.77
(b) 75.09