Answered: Normal distribution. Assume the height…

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

Normal distribution. Assume the height of female 20-29 year-old is normally
distributed with a mean of 65 inches and a standard deviation of 3 inches.
a. What is the probability that a randomly selected girl 20-29 year-old will be 67 inches or
lower?
b. What is the probability that a randomly selected girl 20-29 year-old will be 67 inches or
higher?
c. What is the probability that a randomly selected girl 20-29 year-old will be between 63 and
70 inches?
Suppose a random sample of four 20-29 year-old females is selected.
d. What is the probability that all four will be 67 inches or lower?
e. What is the distribution of the sample mean height of 4 females? Provide all info.
x bar ~ ____________________(___________________,____________________ )
The distribution is [Circle One:] Exact Approximate
Why? _________________________________________________________________
f. What is the probability that the mean height of four will be 66 inches or higher?

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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