uppose that the heights of female adults in the United States are normally distributed with a mean of 65.4 inches and a standard deviation of 2.8 inches. Let X denote the height of a randomly chosen adult female. Illustrate your answers with graphs. a. Use the standard normal probability table to calculate the probability that X is between 66 and 70 inches. b. Suppose that a random sample of 10 adult females was chosen and the sample mean was recorded. Give the values of the mean and standard deviation of the sample mean, and describe the shape of the distribution. c. Use the standard normal probability table to calculate the probability that the sample mean is greater than 68 inches.

uppose that the heights of female adults in the United States are normally distributed with a mean of 65.4 inches and a standard deviation of 2.8 inches. Let X denote the height of a randomly chosen adult female. Illustrate your answers with graphs. a. Use the standard normal probability table to calculate the probability that X is between 66 and 70 inches. b. Suppose that a random sample of 10 adult females was chosen and the sample mean was recorded. Give the values of the mean and standard deviation of the sample mean, and describe the shape of the distribution. c. Use the standard normal probability table to calculate the probability that the sample mean is greater than 68 inches.

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

Suppose that the heights of female adults in the United States are normally distributed with a mean of 65.4
inches and a standard deviation of 2.8 inches. Let X denote the height of a randomly chosen adult female.
Illustrate your answers with graphs.
a. Use the standard normal probability table to calculate the probability that X is between 66 and 70 inches.
b. Suppose that a random sample of 10 adult females was chosen and the sample mean was recorded. Give
the values of the mean and standard deviation of the sample mean, and describe the shape of the distribution.
c. Use the standard normal probability table to calculate the probability that the sample mean is greater than
68 inches.

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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