The breaking strength in kgmm for a certain type of syntheti

The breaking strength (in kg/mm) for a certain type of synthetic fabric commonly used for sutures follows a normal distribution with mean 1.86 and standard deviation 0.27. A simple random sample of 80 pieces of fabric is drawn.
(a) What is the probability that the sample mean breaking strength is less than 1.8 kg/mm? (b) Find the 80th percentile of the sample mean breaking strength. Use fuctions from R on the computer!

Solution

I will provide the results and the corresponding R commands required to get these results.

First we define sample standard deviation ,

> ssd=0.27/sqrt(80)

(a)

> pnorm(1.8 , mean=1.86, sd=0.ssd, lower.tail=TRUE)

pnorm function is used to find the normal probability in R. If you have to find the probability greater than the mean breaking strength then use lower.tail=FALSE.

This gives the probability as, 0.02342709.

(b)

> qnorm(0.8,mean=1.86,sd=ssd)

This gives the 80th percentile as, 1.885406