Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 240 feet and a standard deviation of 42 feet. We randomly sample 49 fly balls.Please label each part ## Part (a)If $ \overline{X} = $ average distance in feet for 49 fly balls, then give the distribution of $ \overline{X} $. Round your standard deviation to two decimal places.$ \overline{X} \sim \text{______} \left( \text{______} , \text{______} \right) $.## Part (b)What is the probability that the 49 balls traveled an average of less than 230 feet? (Round your answer to four decimal places.)[Input box]Sketch the graph. Scale the horizontal axis for $ \overline{X} $. Shade the region corresponding to the probability.There are four normal distribution graphs with the horizontal axis labeled from 225 to 255. Each graph has a different shaded region:1. Top left graph: Shaded region from the start of the axis to just above 250.2. Top right graph: Shaded region from the start of the axis to just below 230.3. Bottom left graph: Entire area under the curve is shaded.4. Bottom right graph: Shaded region beyond 245 to 255.## Part (c)Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)[Input box] ft

Plug in all the values in the formula, we get

Answered: If X = average distance in feet for 49…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 240 feet and a standard deviation of 42 feet. We randomly sample 49 fly balls.

Please label each part

## Part (a)

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

$ \overline{X} \sim \text{______} \left( \text{______} , \text{______} \right) $.

## Part (b)

What is the probability that the 49 balls traveled an average of less than 230 feet? (Round your answer to four decimal places.)

[Input box]

Sketch the graph. Scale the horizontal axis for $ \overline{X} $. Shade the region corresponding to the probability.

There are four normal distribution graphs with the horizontal axis labeled from 225 to 255. Each graph has a different shaded region:

1. Top left graph: Shaded region from the start of the axis to just above 250.
2. Top right graph: Shaded region from the start of the axis to just below 230.
3. Bottom left graph: Entire area under the curve is shaded.
4. Bottom right graph: Shaded region beyond 245 to 255.

## Part (c)

Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

[Input box] 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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