Question

Assume that females have pulse rates that are normally distributed with a mean of u 73.0 beats per minute and a standard deviation ofơ-12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute The probability is 5948 Round to four decimal places as needed) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute The probability is Round to four decimal places as needed)

Answer 1

Let X denote pulse rates for females

a.

We need to find :

$\dpi{100} \small P(X<76) = P\left ( \frac{X-Mean}{SD}<\frac{76-Mean}{SD} \right )$

$\dpi{100} \small = P\left (Z<\frac{76-73}{12.5} \right )$

$\dpi{100} \small = P\left (Z< 0.24\right )$

Using standard normal tables or using the Excel function " NORMSDIST(0.24)" we get :

$\dpi{100} \small P(X<76) = 0.5948$

The probability is 0.5948

b.

$\dpi{100} \small \bar{X}$follows normal distribution with mean = 76 and standard deviation = 12.5 / $\dpi{80} \small \sqrt{4}$

Now, we need to find

$\dpi{100} \small P(\bar{X}<76) = P\left ( \frac{\bar{X}-Mean}{SD/\sqrt{n}}<\frac{76-Mean}{SD/ \sqrt{n}} \right )$

$\dpi{100} \small = P\left ( Z<\frac{76-73}{12.5/ \sqrt{4}} \right )$

$\dpi{100} \small = P(Z<0.48)$

$\dpi{100} \small P(\bar{X}<76) = 0.6844$

The probability is 0.6844