Answered: What women's height corresponds to a…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Assume that women's heights have a distribution that is symmetric and unimodal, with a mean of

inches, and the standard deviation is

2.5

inches. Assume that men's heights have a distribution that is symmetric and unimodal, with mean of

inches and a standard deviation of

inches.

a. What women's height corresponds to a z-score of

−1.80?

b. Professional basketball player Evelyn Akhator is 75 inches tall and plays in the WNBA (women's league). Professional basketball player Draymond Green is 79 inches tall and plays in the NBA (men's league). Compared to his or her peers, who is taller?

Assume that women's heights have a distribution that is symmetric and unimodal, with a mean of 64 inches, and the standard deviation is 2.5 inches. Assume that men's heights have a distribution that is symmetric and unimodal,
with mean of 73 inches and a standard deviation of 2 inches.
a. What women's height corresponds to a Z-score of – 1.80?
b. Professional basketball player Evelyn Akhator is 75 inches tall and plays in the WNBA (women's league). Professional basketball player Draymond Green is 79 inches tall and plays in the NBA (men's league). Compared to his or
her peers, who is taller?
a. The women's height that corresponds to a z-score of – 1.80 is
inches.
(Type an integer or a decimal. Do not round.)
b.
because
is
standard deviations above the mean for
while
is only
standard deviations above the mean for
(Type integers or decimais Tounded to two decimal places as needed.)
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Evelyn Akhator
Draymond Green
Не
She
Men
Women

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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