Answered: Globally, women’s heights are normally…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Question

a) Globally, women’s heights are normally distributed, with a mean of 65 inches and
a standard deviation of 3 inches. Calculate the Z-score for a woman who is 67 inches
tall. This is how many standard deviations this woman is above the average woman
in the world.

b) Calculate the Z-score for a woman who is 61 inches tall.

c) Calculate the original height for a woman with a Z-score of -2.1.

d) Latvia has the tallest women on the planet (on average). Their mean is 67 inches. If
this population of women also has a standard deviation of 3 inches, what is the Z-
score for a 67-inch woman in this population?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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