Answer: 0.2510
Step-by-step explanation:
Given : Mean =[tex]\mu=\text{73.0 beats per minute}[/tex]
Standard deviation : [tex]\sigma=\text{12.5 beats per minute}[/tex]
Sample size : n=1
We assume that females have pulse rates that are normally distributed.
Then , the formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x =69
[tex]z=\dfrac{69-73}{\dfrac{12.5}{\sqrt{1}}}=-0.32[/tex]
For x= 77
[tex]z=\dfrac{77-73}{\dfrac{12.5}{\sqrt{1}}}=0.32[/tex]
The p-value =[tex]P(-0.32<z<0.32)[/tex]
[tex]=P(z<0.32)-P(z<-0.32)\\= 0.6255158-0.3744842\\=0.2510316\approx0.2510[/tex]
Hence, the probability that her pulse rate is between 69 beats per minute and 77 beats per minute =0.2510
The probability that her pulse rate is between 69 beats per minute and 77 beats per minute is 25.1%
Z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
z = (raw score - mean) / standard deviation
Mean = 73, standard deviation = 12.5
For x = 69:
z = (69 - 73) / 12.5 = -0.32
For x = 77:
z = (77 - 73) / 12.5 = 0.32
P(-0.32 <z < 0.32) = P(z < 0.32) - P(z < -0.32) = 0.6255 - 0.3745 = 0.251
The probability that her pulse rate is between 69 beats per minute and 77 beats per minute is 25.1%
Find out more on z score at: https://brainly.com/question/25638875
