Question

a physician wants to estimate with 92% confidence the average height of 6 year old boys in his community he wants his margin of error to be 0.5 in the population of these heights is normally distributed with a standard deviation of 1.8 inches how many 6 year old boy should he use in his sample​

Answer 1

n=40 boys

Explanation:

-Margin of error is given by the formula:

`E=z(\sigma)/(√(n))`

-The z score for a probability of 92% is 1.75

#We make n the subject of the formula and substitute at a 92% confidence:

`E=z(\sigma)/(√(n))\\\\√(n)=(z\sigma)/(E)\\\\n=[(z\sigma)/(E)]^2\\\\\therefore n=[(1.75* 1.8)/(0.5)]^2\\\\=39.69\approx 40`

Hence, he needs approximately 40 boys for the study