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Men's and Women's Heights. The heights of women aged 20-29 in the United States are approximately Normal, with mean \(64.1\) inches and standard deviation \(3.7\) inches. Men the same age have mean height \(69.4\) inches, with standard deviation \(3.1\) inches. \(-\) What are the \(z\)-scores for a woman \(5.5\) feet tall and a man \(5.5\) feet tall? Say in simple language what information the \(z\)-scores give that the original nonstandardized heights do not.

The Medical College Admissions Test. Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). The total score of the four sections on the test ranges from 472 to 528 . In spring of 2019 , the mean score was \(500.9\), with a standard deviation of \(10.6\). a. What are the median and the first and third quartiles of the MCAT scores? What is the interquartile range? b. Give the interval that contains the central \(80 \%\) of the MCAT scores.

To completely specify the shape of a Normal distribution, you must give a. the mean and the standard deviation. b. the five-number summary. c. the median and the quartiles.

The distribution of hours of sleep per weeknight among college students is found to be Normally distributed, with a mean of \(6.5\) hours and a standard deviation of 1 hour. What range contains the middle \(95 \%\) of hours slept per weeknight by college students? a. \(5.5\) and \(7.5\) hours per weeknight b. \(4.5\) and \(7.5\) hours per weeknight c. \(4.5\) and \(8.5\) hours per weeknight

The distribution of hours of sleep per weeknight among college students is found to be Normally distributed, with a mean of \(6.5\) hours and a standard deviation of 1 hour. The percentage of college students that sleep at least eight hours per weeknight is about a. \(95 \%\) b. \(6.7 \%\) c. \(2.5 \%\)

The scores of adults on an IQ test are approximately Normally distributed, with mean 100 and standard deviation 15. Alysha scores 135 on such a test. Her \(z\)-score is about a. \(1.33 .\) b. \(2.33\) c. \(6.33 .\)

The proportion of observations from a standard Normal distribution that take values greater than \(1.78\) is about a. \(0.9554 .\) b. \(0.0446 .\) c. \(0.0375 .\)

Heights of Men and Women. The heights of women aged 20-29 follow approximately the \(N(64.1,3.7)\) distribution. Men the same age have heights distributed as \(N(69.4,3.1)\). What percentage of men aged 20-29 are taller than the mean height of women aged 20-29?

Weights Aren't Normal. The heights of people of the same sex and similar ages follow a Normal distribution reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of men aged 20-29 in the United States have mean 186.8 pounds and median \(177.8\) pounds. The first and third quartiles are \(152.9\) pounds and \(208.5\) pounds, respectively. In addition, the bottom \(10 \%\) have weights less than or equal to \(137.6\) pounds while the top \(10 \%\) have weights greater than or equal to 247.2. What can you say about the shape of the weight distribution? Why?