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# Professor gave a statistics test. The scores follow the

### Customer Question

Professor Moore gave a statistics test. The scores follow the distribution: \muμ = 22 and \sigmaσ = 4.What is the probability that a single student randomly chosen from all of those taking the test scores 18 or lower? Express as a percent rounded to the nearest hundredth.%Now take an SRS of 8 students who took the test. What are the mean and standard deviation of the sampling distribution of 8 students? Round to the nearest thousandth.\mu_{x\:}=
\sigma_x=σx=What is the probability that the average of the tests for these 8 students is 18 or lower? Express as a percent rounded to the nearest hundredth.%
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Submitted: 5 months ago.
Category: Calculus and Above
Expert:  Ryan replied 5 months ago.

Hi,

Thank you for using the site. I'll be happy to help you with these problems.

For the first problem:

z = (x - µ)/sigma = (18 - 22)/4 = -1.00

P(x < 18) = P(z < -1) = 0.1587 = 15.87%

For the second problem:

mu_{x\:}= 22

sigma_x=σx= 4/√8 = 1.414

z = (x-bar - µ) / (sigma / √n) = (18 - 22) / (4 / √8) = -2.8284

P(x-bar < 18) = P(z < -2.8284) = 0.0023 = 0.23%