The length of a movie file that is available for streaming is modeled using the normal distribution shown below. The mean of the distribution is 189.7 min and the standard deviation is 20.2min.In the figure, there are three missing values to fill in along the axis. The middle value is under the highest part of the curve. And, the left and right values are each the same distance away from the middle value.Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and fill in the missing values along the axis. The image displays a bell curve representing a normal distribution. It features a dropdown menu labeled "Percentage of total area shaded," with options for 68%, 95%, and 99.7%, highlighting the different standard deviations in a normal distribution.### Graph Description:- **Horizontal Axis (X-axis):** Labeled "Time (in min)," it ranges from 120 to 260.- **Vertical Curved Line:** Represents the probability density function of the normal distribution.- **Vertical Dashed Lines:** Indicate the range within one standard deviation from the mean when 68% of the area is selected.- **Shaded Area:** Corresponds to the selected percentage of the total area under the curve, centered around the mean.This graph illustrates the concept of standard deviation in a normal distribution, where:- 68% of the data falls within one standard deviation,- 95% within two,- 99.7% within three.This visual aids users in understanding how different percentages of data are distributed around the mean.

We want to find the probability by using Emperical rule Result: By emperical rule…

Answered: Percentage of total area shaded: 68%…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The length of a movie file that is available for streaming is modeled using the normal distribution shown below. The mean of the distribution is 189.7 min and the standard deviation is 20.2min.

In the figure, there are three missing values to fill in along the axis. The middle value is under the highest part of the curve. And, the left and right values are each the same distance away from the middle value.

Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and fill in the missing values along the axis.

The image displays a bell curve representing a normal distribution. It features a dropdown menu labeled "Percentage of total area shaded," with options for 68%, 95%, and 99.7%, highlighting the different standard deviations in a normal distribution.

### Graph Description:
- **Horizontal Axis (X-axis):** Labeled "Time (in min)," it ranges from 120 to 260.
- **Vertical Curved Line:** Represents the probability density function of the normal distribution.
- **Vertical Dashed Lines:** Indicate the range within one standard deviation from the mean when 68% of the area is selected.
- **Shaded Area:** Corresponds to the selected percentage of the total area under the curve, centered around the mean.

This graph illustrates the concept of standard deviation in a normal distribution, where:
- 68% of the data falls within one standard deviation,
- 95% within two,
- 99.7% within three.

This visual aids users in understanding how different percentages of data are distributed around the mean.

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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Percentage of total area shaded: 68% 68% 95% 99.7% 120 140 160 180 200 220 240 260 Time (in min)