Teens have pulse rates that are Normally Distributed with a

Teens have pulse rates that are Normally Distributed with a mean (w) = 77.5 beats per minutes and a standard deviation (sigma) = 11.6 beats per minutes:

Find the percentiles P1 and P99

Find the probability that 25 Randomly selected teens have a mean (w) pulse rate between 70 and 85 beats per minutes.

Solution

Given mean(W)=77.5 beats per minutes

Standard deviation (sigma)=11.6 beats per minute

Percentiles:

P1=mean-2.33*S.D

P1=77.5-2.33*11.6=50.472

P99= mean+2.33*S.D

P99= 77.5+2.33*11.6=104.528

Probability that randomly selected teens have a mean pulse rate between 70 and 85 beats per minutes is

P(70<x<85)=P(<Z<)=P(-0.65<z<0.65)=0.74-0.26=0.48