The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (source: american dietetic association). if a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.

Question

Mathematics

Nikolas Duffy

23 March, 02:40

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (source: american dietetic association). if a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.

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Honeybun · Answer 1

Given:

Mean, μ = 196

Std. dev., σ = 22

A sample size of 50 (> 30) is large enough to provide meaningful data.

The random variable is x = 200.

The z-score is

z = (x - μ) / σ = (200 - 196) / 22 = 0.1818

From normal distribution tables, obtain

Prob (X < 200) = 0.572 = 57.2%

Answer: 57.2%