Question

The wildlife department has been feeding a special food to rainbow trout fingerlings. Based on a large number of observations, the weight of the trout are normally distributed with a mean of 402.7 grams and a standard deviation of 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

Answer 1

Answer: 0.0222

Step-by-step explanation:

Given : The wildlife department has been feeding a special food to rainbow trout fingerlings.

Based on a large number of observations, the weight of the trout are normally distributed with

Mean : $\mu=402.7\text{ grams}$

Standard deviation : $\sigma=8.8\text{ grams}$

Sample size : = 40

Let x be the random variable that represents the weight of the trout .

Z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x=405.5 grams

$z=\dfrac{405.5-402.7}{\dfrac{8.8}{\sqrt{40}}}\approx2.01$

By using standard normal distribution table , the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams :-

$P(405.52.01)=1-P(z$