The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean o

Question

3 years ago

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The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean o

f 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds

Mathematics

1 answer:

prohojiy [21] · Answer 1 · 2022-04-24T20:06:31+03:00

Answer:

The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%

Step-by-step explanation:

For a normal random variable with mean Mu = 3.2 and standard deviation sd = 0.8 there is a distribution of the sample mean (MX) for samples of size 4, given by:

Z = (MX - Mu) / sqrt (sd ^ 2 / n) = (MX - 3.2) / sqrt (0.64 / 4) = (MX - 3.2) / 0.4

For a sample mean of 3.0, Z = (3 - 3.2) / 0.4 = -0.5

For a sample mean of 3.0, Z = (4 - 3.2) / 0.4 = 2.0

P (3.2 <MX <4) = P (-0.5 < Z <2.0) = 0.6687.

The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%