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Answer :
The probability that the mean weight of a sample of twenty freshmen will be greater than 145 pounds is 0.138.
What is the probability?
The probability is determined using the central limit theorem and the formula for the standard error of the mean:
- SE = σ/√n
where;
- SE is the standard error of the mean,
- σ is the population standard deviation, and
- n is the sample size.
Data given;
σ = 12.3 pounds; n = 20
SE = 12.3/√20
SE = 2.75 pounds.
The sample mean is then standardized using the z-score formula:
z = (x - μ) / SE
z = (145 - 142) / 2.75
z = 1.09
Using a calculator, the probability of a z-score greater than 1.09 is 0.138.
Learn more about probability at: https://brainly.com/question/24756209
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