WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes.What is the probability that a particular listener will tune in: More than 20 minutes? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.) For 20 minutes or less? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.) Between 10 and 12 minutes? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

1. The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the…

Answered: WNAE, an all-news AM station, finds…

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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WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes.

What is the probability that a particular listener will tune in:

More than 20 minutes? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

For 20 minutes or less? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

Between 10 and 12 minutes? (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

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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