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

Question

Quizplus · Accepted Answer

We need to calculate the z-score using the formula:
z = (x̄ - μ)/(σ/√n)
Here, x̄ = 3.4 pounds, μ = 3.2 pounds, σ = 0.8 pound, n = 64
z = (3.4 - 3.2)/(0.8/√64) = 2
Using a standard normal distribution table or a calculator, we can find the probability of obtaining a z-score of 2 or more (i.e., sample mean this large or larger) as 0.0228 (rounded to four decimal places). 
Therefore, the answer is C.

The Owner of a Fish Market Has an Assistant Who