Answer to Question #295997 in Statistics and Probability for partha ray

Question #295997

the dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are apporoximately normally distributed with a mean 72 and a standard deviation of 4 based of this information,what is the probability that the mean score of a sample of 64 students it at least 73


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Expert's answer
2022-02-10T16:35:33-0500

Let X=X= the mean score of a sample: XN(μ,σ2/n).X\sim N(\mu, \sigma^2/n).

Given μ=72,σ=4,n=64.\mu=72, \sigma=4, n=64.


P(X73)=1P(X<73)P(X\ge 73)=1-P(X<73)

=1P(Z<73724/64)=1P(Z<2)=1-P(Z<\dfrac{73-72}{4/\sqrt{64}})=1-P(Z<2)

0.02275\approx 0.02275

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