Question

Assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minutes. If 16 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.

Answer 1

Answer: 0.9726

Step-by-step explanation:

Given :  Females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minutes.

i.e. $\mu=74$ and $\sigma=12.5$

Let x is a random variable to represent the pulse rates.

Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For n= 16 , the probability that her pulse rate is less than 80 beats per minute will be :-

$P(x<80)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{80-74}{\dfrac{12.5}{\sqrt{16}}})\\\\=P(z<\dfrac{6}{\dfrac{12.5}{4}})\\\\=P(z<\dfrac{24}{12.5})\\\\=P(z<1.92)=0.9726\ \ [\text{By using z-table.}]$

Hence, the required probability = 0.9726