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One of the consequences of the rise of music streaming services is that song lengths have decreased in the last few years. Suppose the length in seconds, X, of a randomly chosen Billboard Hot 100 song can be modeled with a Normal distribution with mean of 210 seconds and 1. standard deviation of 70 seconds. а. According to the model, the longest 15% of songs are at least how many seconds long? b. What is the probability that a randomly chosen song from the Hot 100 list lasts longer than 4 mınutes? ) Suppose you randomly choose 4 songs from the Hot 100 list. What is the probability that the average song length is between 2 and 3 minutes? C.

One of the consequences of the rise of music streaming services is that song lengths have decreased in the last few years. Suppose the length in seconds, X, of a randomly chosen Billboard Hot 100 song can be modeled with a Normal distribution with mean of 210 seconds and 1. standard deviation of 70 seconds. а. According to the model, the longest 15% of songs are at least how many seconds long? b. What is the probability that a randomly chosen song from the Hot 100 list lasts longer than 4 mınutes? ) Suppose you randomly choose 4 songs from the Hot 100 list. What is the probability that the average song length is between 2 and 3 minutes? C.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. One of the consequences of the rise of music streaming services is that song lengths have decreased in the last few years. Suppose the length in seconds, X, of a randomly chosen Billboard Hot 100 song can be modeled with a Normal distribution with a mean of 210 seconds and a standard deviation of 70 seconds. a. According to the model, the longest 15% of songs are at least how many seconds long? b. What is the probability that a randomly chosen song from the Hot 100 list lasts longer than 4 minutes? c. Suppose you randomly choose 4 songs from the Hot 100 list. What is the probability that the average song length is between 2 and 3 minutes? d. What are the mean and standard deviation of the total length of four randomly chosen Hot 100 songs? Hint: Define a random variable for each of the four songs. e. In order to calculate the standard deviation in the previous part of the problem, you must make an assumption about the lengths of the four songs. What is that assumption, and what in the description from part c tells you that you can make that assumption?
Transcribed Image Text:1. One of the consequences of the rise of music streaming services is that song lengths have decreased in the last few years. Suppose the length in seconds, X, of a randomly chosen Billboard Hot 100 song can be modeled with a Normal distribution with a mean of 210 seconds and a standard deviation of 70 seconds. a. According to the model, the longest 15% of songs are at least how many seconds long? b. What is the probability that a randomly chosen song from the Hot 100 list lasts longer than 4 minutes? c. Suppose you randomly choose 4 songs from the Hot 100 list. What is the probability that the average song length is between 2 and 3 minutes? d. What are the mean and standard deviation of the total length of four randomly chosen Hot 100 songs? Hint: Define a random variable for each of the four songs. e. In order to calculate the standard deviation in the previous part of the problem, you must make an assumption about the lengths of the four songs. What is that assumption, and what in the description from part c tells you that you can make that assumption?
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