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

Answer:

n=40 boys

Step-by-step explanation:

-Margin of error is given by the formula:

$E=z\frac{\sigma}{\sqrt{n}}$

-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:

$E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=\frac{z\sigma}{E}\\\\n=[\frac{z\sigma}{E}]^2\\\\\therefore n=[\frac{1.75\times 1.8}{0.5}]^2\\\\=39.69\approx 40$

Hence, he needs approximately 40 boys for the study