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=(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,

Substitute the values and simplify,

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