Prince Edward Island Fisheries and Environment has been feeding a special food to rainbow trout fingerlings in a pond. A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?
A) 0.3783
B) 0.0228
C) 1.0
D) 0.5

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the sampling distribution of the sample mean. The central limit theorem states that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normal with mean μ (402.7 grams) and standard deviation σ/√n (8.8 grams/√40 ≈ 1.39 grams). 
Now, we need to standardize the sample mean using the formula: z = (x̄ - μ) / (σ/√n) = (405.5 - 402.7) / (1.39) ≈ 1.99. 
The probability that the mean weight for a sample of 40 trout exceeds 405.5 grams is equivalent to the probability of getting a sample mean more extreme than 405.5 grams, which corresponds to a z-score greater than 1.99. Using a standard normal table or a calculator, we can find that the probability is approximately 0.0228. Therefore, the best choice is B.

Prince Edward Island Fisheries and Environment Has Been Feeding a Special