The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram.
-If a sample of 64 fish yields a mean of 3.4 kilograms,what is the probability of obtaining a sample mean this large or larger?
A) 0.4987
B) 0.0001
C) 0.0013
D) 0.0228

Question

Quizplus · Accepted Answer

We need to use the central limit theorem, which states that if we have a sample of 64 or more, the distribution of sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the sample mean is 3.4 kilograms, which is (3.4 - 3.2) / (0.8 / sqrt(64)) = 2, so the probability of obtaining a sample mean this large or larger can be found by looking up the area to the right of a z-score of 2 in a standard normal distribution table.

This area is approximately 0.0228, so the answer is D.

The Owner of a Fish Market Has an Assistant Who