SOLUTION: It is known that the weights of apples from a farm are normally distributed. In order to estimate the mean weight, a random sample of 150 apples is considered and the sample mean a

Question 1170808: It is known that the weights of apples from a farm are normally distributed. In order to estimate the mean weight, a random sample of 150 apples is considered and the sample mean and population standard deviation are 6 kg and 0.8 kg respectively.
(a) Construct a 95% confidence interval estimate for the population mean weight of apples.
(b) The researcher suggests doing the study again so that 98% confidence interval estimate for the population mean weight of apples is (5.8835,6.1165) kg. How large should the sample size be?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the half-interval is z(0.975)*sigma/sqrt(n)=1.96*0.8/sqrt(150)
=0.128, which is subtracted from and added to the mean
(5.872, 6.128) units kg
here, the error is 0.1165, and that equals z(0.99)*0.8/sqrt(n)
so 0.1165 *sqrt(n)=2.326*0.8=1.8608
divide both sides by 0.1165 and square the answer, which is 255.12 or 256 apples.
Because a lot of these problems don't round the z-value, which I have, I always go back on the calculator and do a CI check of both n=255 (closest) and n=256 (rounding up, conservative).
n=255 gives the answer exactly.

RELATED QUESTIONS
It is known that the weights of apples from a farm are normally distributed. In order to... (answered by CPhill)

Airlines have to estimate the weights of passengers. Assume that men have weights that... (answered by stanbon)

The weights (in kg) of the students in a school is normally distributed with standard... (answered by VFBundy)

a manufacturing process produces items whose weights are normally distributed . it is... (answered by rothauserc)

birth weights are normally distributed with the mean of 3570g and a standard deviation of (answered by stanbon)

Birth weights are normally distributed with a mean of 3421g and a standard deviation of... (answered by ewatrrr)

Assuming that the weights of newborn babies are normally distributed with mean 6.5 lbs... (answered by Theo)

A food shop buys organic oats in bags of mean weight 1000 grams. It is known that the... (answered by Boreal)

he weight of potatoes produced by one particular farm are found to be... (answered by Boreal)