Question

The waist circumference of males 20-29 years old is approximately normally distributed, with mean 36.4 inches and standard deviation of 5.4.

a.Determine the proportion of 20-29 year old males whose waist circumference is greater than 39.4 in. You must show your work and/or give supporting evidence in order to receive credit.Round the proportion to four decimal places.

b.Determine the waist circumference that is at the 10th percentile. You must show your work and/or give supporting evidence in order to receive credit.Round the circumference to the nearest tenth

Answer 1

Let X:The waist circumference of male

a) To find the proportion of students we need to find the probability of

converting this to standard normal

Where z follows standard normal distribution.

The standard normal probability is calculated using R software.

b)

Let t be the waist circumference that is at the 10th percentile.

That is

Again standardising these

So the point below which the probability of standard normal variate is 0.10 is found out using the normal tables or R software

So

Therefore

Therfore the waist circumference that is at 10th percentile is 29.5.

Thank you !!