Question

Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per minute and a standard deviation of σ=12.5 beats per minute.
a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 68 beats per minute and 80 beats per minute.

Answer 1

Answer:

36.88% probability that her pulse rate is between 68 beats per minute and 80 beats per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 74, \sigma = 12.5$

Between 68 beats per minute and 80 beats per minute.

pvalue of Z when X = 80 subtracted by the pvalue of Z when X = 68. So

X = 80

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{80 - 74}{12.5}$

$Z = 0.48$

$Z = 0.48$ has a pvalue of 0.6844

X = 68

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{68 - 74}{12.5}$

$Z = -0.48$

$Z = -0.48$ has a pvalue of 0.3156

0.6844 - 0.3156 = 0.3688

36.88% probability that her pulse rate is between 68 beats per minute and 80 beats per minute.