Question

Heart Rates For a certain group of individuals, the average heart rate is 74 beats per minute. Assume the variable is normally distributed and the standarddeviation is 2 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate. Use a graphing calculator.Round the answers to four decimal places.Between 71 and 75 beats per minute.P (71

Answer 1

Let X be the number of heartbeats of any individual in the group.

The variable X is normally distributed with mean 74 beats per minute,

$\mu=74$

The standard deviation is 2 beats per minute,

$\sigma=2$

Consider the formula of z-score corresponding to any value of X=x as,

$z=\frac{x-\mu}{\sigma}$

It is required to find the probability that the number of heartbeats of a randomly selected person lies between 71 and 75.

This can be obtained as follows,

$\begin{gathered} P(71From the Standard Normal Distribution Table,[tex]\begin{gathered} \phi(0.5)=0.1915 \\ \phi(1.5)=0.4332 \end{gathered}$

Substitute the values and simplify,

$\begin{gathered} =0.4332+0.1915 \\ =0.6247 \end{gathered}$