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.
Accepted Solution
A:
Answer: 0.9726Step-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. [tex]\mu=74[/tex] and [tex]\sigma=12.5[/tex]Let x is a random variable to represent the pulse rates.Formula : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For n= 16 , the probability that her pulse rate is less than 80 beats per minute will be :-[tex]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.}][/tex]Hence, the required probability = 0.9726