Question

The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 5.99 ounces and a standard deviation of 0.21 ounce. Suppose that you draw a random sample of 43 cans. Find the probability that the mean weight of the sample is less than 5.98 ounces.

Answer 1

Answer: 0.0075

Explanation:

Given : The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with

`\mu=5.99\text{ ounces}`

`\sigma=0.21\text{ ounces}`

Sample size : n=43

Z-score :
`z=(x-\mu)/(\sigma)`

For x= 5.98

`z=(5.48-5.99)/(0.21)\approx-2.43`

By using standard normal distribution table table , the probability that the mean weight of the sample is less than 5.98 ounces will be :_

`P(x<5.98)=P(z<-2.43)=0.0075494\approx0.0075`

Hence, the probability that the mean weight of the sample is less than 5.98 ounces = 0.0075