The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 42 million and a standard deviation of 7 million. What is the probability next week’s show will: Have between 40 and 45 million viewers? Have at least 50 million viewers? Exceed 40 million viewers?

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 42 million and a standard deviation of 7 million. What is the probability next week’s show will: Have between 40 and 45 million viewers? Have at least 50 million viewers? Exceed 40 million viewers?

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

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 42 million and a standard deviation of 7 million. What is the probability next week’s show will:
Have between 40 and 45 million viewers?
Have at least 50 million viewers?
Exceed 40 million viewers?

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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