Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 48 feet. We randomly sample 49 fly balls.Part A. B. C. are listed in the included images. **Part (a)**If \( \bar{X} \) = average distance in feet for 49 fly balls, then give the distribution of \( \bar{X} \). Round your standard deviation to two decimal places.\[ \bar{X} \sim N \left( 250, 0.50 \right) \]This notation represents that the average distance \( \bar{X} \) follows a normal distribution with a mean (\( \mu \)) of 250 feet and a standard deviation (\( \sigma \)) of 0.50 feet. **Part (b)**What is the probability that the 49 balls traveled an average of less than 242 feet? (Round your answer to four decimal places.)**Answer: 0.0606**Sketch the graph. Scale the horizontal axis for \( \bar{X} \). Shade the region corresponding to the probability.There are four bell-shaped curves, all depicting normal distributions with a range from 230 to 270 on the horizontal axis. Each curve has different regions shaded to illustrate probabilities:1. **Top Left Graph**: The area to the left of approximately 242 is shaded, indicating the probability of the balls traveling an average of less than 242 feet.2. **Top Right Graph**: This graph has a different shaded region, focusing on the right end of the curve.3. **Bottom Left Graph**: Similar to the first graph, but with a different focus on shading within the distribution.4. **Bottom Right Graph**: This shows an alternate shading pattern yet again, with focus on the central area.---**Part (c)**Find the 60th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)**Answer: [Blank] ft**

Given: n = 49 μ = 250 σ = 48 Formula Used: μx = μ σx = σn Z = X-μxσx

Answered: Suppose that the distance of fly balls…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 48 feet. We randomly sample 49 fly balls.

Part A. B. C. are listed in the included images.

**Part (a)**

If \( \bar{X} \) = average distance in feet for 49 fly balls, then give the distribution of \( \bar{X} \). Round your standard deviation to two decimal places.

\[ \bar{X} \sim N \left( 250, 0.50 \right) \]

This notation represents that the average distance \( \bar{X} \) follows a normal distribution with a mean (\( \mu \)) of 250 feet and a standard deviation (\( \sigma \)) of 0.50 feet.

**Part (b)**

What is the probability that the 49 balls traveled an average of less than 242 feet? (Round your answer to four decimal places.)

**Answer: 0.0606**

Sketch the graph. Scale the horizontal axis for \( \bar{X} \). Shade the region corresponding to the probability.

There are four bell-shaped curves, all depicting normal distributions with a range from 230 to 270 on the horizontal axis. Each curve has different regions shaded to illustrate probabilities:

1. **Top Left Graph**: The area to the left of approximately 242 is shaded, indicating the probability of the balls traveling an average of less than 242 feet.

2. **Top Right Graph**: This graph has a different shaded region, focusing on the right end of the curve.

3. **Bottom Left Graph**: Similar to the first graph, but with a different focus on shading within the distribution.

4. **Bottom Right Graph**: This shows an alternate shading pattern yet again, with focus on the central area.

---

**Part (c)**

Find the 60th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

**Answer: [Blank] ft**

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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