The wildlife department 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 need to use the Central Limit Theorem here since the population standard deviation is known and the sample size is large (n = 40). The z-score for a sample mean of 405.5 grams is calculated as:

z = (X̄ - μ) / (σ / sqrt(n))

z = (405.5 - 402.7) / (8.8 / sqrt(40)) = 2.1

Using a standard normal distribution table or calculator, we can find the probability that a z-score is greater than 2.1, which is approximately 0.0228. Therefore, the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams is 0.0228 or 2.28%.

The Wildlife Department Has Been Feeding a Special Food to Rainbow