Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 230 feet and a standard deviation of 46 feet. Let X = distance in feet for a fly ball.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 230 feet and a standard deviation of 46 feet. Let X = distance in feet for a fly ball.
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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Please label each part
![**Normal Distribution of Fly Ball Distances**
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 230 feet and a standard deviation of 46 feet. Let \( X \) = distance in feet for a fly ball.
**Part (a)**
Give the distribution of \( X \).
\[ X \sim N(\text{mean}, \text{standard deviation}) \]
**Part (b)**
If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 180 feet? (Round your answer to four decimal places.)
\[ \text{Probability} = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba3fd56c-d0e8-48f8-a096-874bc7ee8436%2Fb1d734b6-c346-44d8-9144-41f5124bc3ab%2Fcyomka_processed.png&w=3840&q=75)
Transcribed Image Text:**Normal Distribution of Fly Ball Distances**
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 230 feet and a standard deviation of 46 feet. Let \( X \) = distance in feet for a fly ball.
**Part (a)**
Give the distribution of \( X \).
\[ X \sim N(\text{mean}, \text{standard deviation}) \]
**Part (b)**
If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 180 feet? (Round your answer to four decimal places.)
\[ \text{Probability} = \]
![**Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.)**
[Text box for input] ft
**Sketch the graph.**
There are four bell-shaped graphs shown:
1. **Graph 1:** No shaded area, centered around 250 on the x-axis.
2. **Graph 2:** No shaded area, centered around 250 on the x-axis.
3. **Graph 3 (Selected):** The bell-shaped curve is shaded up to approximately 280 on the x-axis, indicating the 80th percentile.
4. **Graph 4:** The bell-shaped curve is shaded further right compared to Graph 3, beyond 300 on the x-axis.
**Write the probability statement. (Let \( k \) represent the score that corresponds to the 80th percentile.)**
\( P(X < k) = \) [Text box for input]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba3fd56c-d0e8-48f8-a096-874bc7ee8436%2Fb1d734b6-c346-44d8-9144-41f5124bc3ab%2Fo1lp1vv_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.)**
[Text box for input] ft
**Sketch the graph.**
There are four bell-shaped graphs shown:
1. **Graph 1:** No shaded area, centered around 250 on the x-axis.
2. **Graph 2:** No shaded area, centered around 250 on the x-axis.
3. **Graph 3 (Selected):** The bell-shaped curve is shaded up to approximately 280 on the x-axis, indicating the 80th percentile.
4. **Graph 4:** The bell-shaped curve is shaded further right compared to Graph 3, beyond 300 on the x-axis.
**Write the probability statement. (Let \( k \) represent the score that corresponds to the 80th percentile.)**
\( P(X < k) = \) [Text box for input]
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