A study is interested in the change in resting heart-rate for people in their tw

Question

A study is interested in the change in resting heart-rate for people in their twenties, ten minutes after drinking 6 ounces of coee. Suppose that the change in heart-rate for these people is normally distributed with mean 7:3 beats per minute, and standard deviation 11.1. Let Y be the change in heart rate for a randomly chosen person. (a) Find P(Y > 10).

(b) In what percentage of people did the resting heart rate after drinking the coee actually go down?

(c) Now suppose three people are chosen at random: (i) What is the probability that all 3 saw a change in heart rate greater than 20 beats per minute? (ii) What is the probability that the average heart rate change for the group of three was more than 20 beats per minute?

Explanation / Answer

as from normal distribution z score =(X-mean)/std deviation

hence a)P(Y>10) =1-P(Y<10) =1-P(Z<(10-7.3)/11.1)=1-P(Z<0.2432)=1-0.5961=0.4039

b)P(X<0) =P(Z<(0-7.3)/11.1)=P(Z<-0.6577)=0.2554

c)probabilty that an individual saw change in heart rate greater then 20bpm=P(X>20) =1-P(Z<1.144)=1-0.8737

=0.1263

hence probability that all 3 saw a change in heart rate greater than 20 beats per minute =(0.1263)3=0.0020

d)for 3 people average mean =20

and std error of mean =std deviation/(n)1/2=6.4086

hence P(X>20)=1-P(X<20)=1-P(Z<(20-7.3)/6.4086)=1-P(Z<1.9817)=1-0.9762=0.0238

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