Question

Weight of chickens has a population standard deviation of 7.5 Lb. Farmer James plans to take a sample of chickens in order to estimate the mean weight (of all chickens).

A. If he samples 50 chickens what is the probability that his sampling error will not exceed 0.8 Lb?

B. Farmer James wants the probability in part a to be at least 0.80, so he decides to double the sample size to 100 chickens. Would is make the desired probability greater than 0.80?

Answer 1

A)

Let X denote the weight of the chickens (in lbs).

Using Central Limit theorem, we know,

Required probability =

B)

Using Central Limit theorem, we know,

Required probability =

This probability is les than 0.80.