The pulse rate for a particualr population of young men have a mean of 65 beats/

Question

The pulse rate for a particualr population of young men have a mean of 65 beats/min and a standard deviation of 6 beats/min. Assume the pulse rates approximately follow a normal distribution. Using R, compute what percentage of young men have the following pulse rates. Hint: you can write a formula in R that will convert the values of interest to z-scores.

a) greater than 50 beats/min?

b) between 68 and 74 beats/min?

c) greater than 1.75 standar deviation from the mean (in either direction)?

I need to see all the R formulas in order to fully understand! Thank you!!!

Explanation / Answer

Ans:

a)pnorm(50, mean=65, sd=6, lower.tail=FALSE)

(above command will directly return P(x>50)=0.9938)

z=(50-65)/6=-2.5

P(z>-2.5)=0.9938

b)P(68<x<74)=P(x<74)-P(x<68)

pnorm(74, mean=65, sd=6, lower.tail=TRUE)

0.9332

pnorm(68, mean=65, sd=6, lower.tail=TRUE)

0.6915

Now,subtract:

P(x<74)-P(x<68)=P(z<1.5)-P(z<0.5)=0.9332-0.6915=0.2417

c)P(z>1.75 or z<-1.5)=P(z<-1.75)+P(z>1.75)=2*P(z<-1.75)=2*0.0401=0.0802

(or use pnorm with mean=0,sd=1)

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