The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 113 minutes and a standard deviation of 14.04 minutes. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 69 movies has a mean runtime less than 118.1 minutes. PHI< 118.1) Find the probabitity that a random sample of 69 movies has a mean runtime between 108.6 and 111.6 minutes. P(108.6 < a < 111.6) =
The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 113 minutes and a standard deviation of 14.04 minutes. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 69 movies has a mean runtime less than 118.1 minutes. PHI< 118.1) Find the probabitity that a random sample of 69 movies has a mean runtime between 108.6 and 111.6 minutes. P(108.6 < a < 111.6) =
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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#27 I just need help with the part circled in red please. Thank you
![**Educational Website Content:**
### Understanding Movie Runtime Distributions
The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 113 minutes and a standard deviation of 14.04 minutes. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.
**Problem 1:**
Find the probability that a random sample of 69 movies has a mean runtime less than 118.1 minutes.
\[ P(\bar{x} < 118.1) \]
**Solution:**
The solution involves calculating the probability using the normal distribution adjusted for the sample size.
---
**Problem 2:**
Find the probability that a random sample of 69 movies has a mean runtime between 108.6 and 111.6 minutes.
\[ P(108.6 < \bar{x} < 111.6) \]
**Solution:**
The methodology involves determining the probabilities for the specified range using the sample's adjusted standard deviation and mean.
---
These problems utilize concepts of sample distributions and standard deviations to calculate probabilities related to movie runtimes, providing practical applications for theoretical statistical concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec7d0b78-7026-4f2e-9cd3-9f6affde891c%2Fa0fb6aed-87ff-4be7-b17d-f37427a928f2%2Fo2s48tc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content:**
### Understanding Movie Runtime Distributions
The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 113 minutes and a standard deviation of 14.04 minutes. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.
**Problem 1:**
Find the probability that a random sample of 69 movies has a mean runtime less than 118.1 minutes.
\[ P(\bar{x} < 118.1) \]
**Solution:**
The solution involves calculating the probability using the normal distribution adjusted for the sample size.
---
**Problem 2:**
Find the probability that a random sample of 69 movies has a mean runtime between 108.6 and 111.6 minutes.
\[ P(108.6 < \bar{x} < 111.6) \]
**Solution:**
The methodology involves determining the probabilities for the specified range using the sample's adjusted standard deviation and mean.
---
These problems utilize concepts of sample distributions and standard deviations to calculate probabilities related to movie runtimes, providing practical applications for theoretical statistical concepts.
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