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In: Statistics and Probability

The weights of the fish in a certain lake are normally distributed with a mean of...

The weights of the fish in a certain lake are normally distributed with a mean of 13 pounds and a standard deviation of 6. If a sample of 9 fish are randomly selected, what is the probability that the mean weight will be between 10.2 and 16.6 pounds?

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Expert Solution

Let , , n=9

Now , the sampling distribution of the sample mean is approximately normally distributed with mean and standard deviation

Now , we want find the probability that the mean weight will be between 10.2 and 16.6 pounds.

Therefore ,

; From standard normal distribution table

Therefore , the probability that the mean weight will be between 10.2 and 16.6 pounds is 0.8833

orchestra answered 2 years ago
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