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

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=(x-\mu)/((\sigma)/(√(n)))`

For x=405.5 grams

`z=(405.5-402.7)/((8.8)/(√(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(405.5<X)=P(z>2.01)=1-P(z<2.01)\\\\=1-0.9777844=0.0222156\appprox0.0222`