need help with this, need answers for A B C D E F thanks! **Understanding Wave Crash Intervals Through Uniform Distribution**In today's lesson, we will examine the intervals at which waves crash on the beach. Given that waves are crashing onto the beach every 4.5 seconds, we will observe the time from when a person arrives at the shoreline until a crashing wave is noted, which follows a Uniform Distribution from 0 to 4.5 seconds. All calculations will be rounded to four decimal places when necessary.1. **Mean and Standard Deviation of Distribution** - a. The mean of this distribution is **\[ \mu \]**. - b. The standard deviation is **\[ \sigma \]**.2. **Probability Calculations** - c. The probability that a wave will crash onto the beach exactly 1.7 seconds after a person arrives is:\[ P(x = 1.7) = \text{0} \] - d. The probability that a wave will crash onto the beach between 1.5 and 3.9 seconds after a person arrives is: \[ P(1.5 < x < 3.9) = \] - e. The probability that it will take longer than 1 second for the wave to crash onto the beach after a person arrives is: \[ P(x \geq 1) = \]3. **Quartile Analysis** - f. Find the maximum for the lower quartile: **\[ Q_1 = \]** seconds.**Visual Aids:**- The graph depicts a uniform distribution ranging from 0 to 4.5 seconds.- A horizontal axis represents time in seconds, while the vertical axis represents the probability density function.- Various intervals of interest (like point probability, specific intervals, and quartile information) are marked on the graph.**Formulas to Utilize:**For a uniform distribution \( U(a, b) \): - Mean \( \mu = \frac{a + b}{2} \) - Standard deviation \( \sigma = \frac{(b - a)}{\sqrt{12}} \) - Probability for a range \( P(c < X < d) = \frac{d-c}{b-a} \)

Answered: Image /qna-images/answer/d3a6c94a-5d86-4ec3-89ba-7cdf3e04e5d4.jpg

a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 1.7 seconds after the person arrives is P(x = 1.7) = d. The probability that the wave will crash onto the beach between 1.5 and 3.9 seconds after the person arrives is P(1.5 1) - f. Find the maximum for the lower quartile. seconds.

a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 1.7 seconds after the person arrives is P(x = 1.7) = d. The probability that the wave will crash onto the beach between 1.5 and 3.9 seconds after the person arrives is P(1.5 1) - f. Find the maximum for the lower quartile. seconds.

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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need help with this, need answers for A B C D E F thanks!

**Understanding Wave Crash Intervals Through Uniform Distribution**

In today's lesson, we will examine the intervals at which waves crash on the beach. Given that waves are crashing onto the beach every 4.5 seconds, we will observe the time from when a person arrives at the shoreline until a crashing wave is noted, which follows a Uniform Distribution from 0 to 4.5 seconds. All calculations will be rounded to four decimal places when necessary.

1. **Mean and Standard Deviation of Distribution**
- a. The mean of this distribution is **\[ \mu \]**.
- b. The standard deviation is **\[ \sigma \]**.

2. **Probability Calculations**
- c. The probability that a wave will crash onto the beach exactly 1.7 seconds after a person arrives is:\[ P(x = 1.7) = \text{0} \]
- d. The probability that a wave will crash onto the beach between 1.5 and 3.9 seconds after a person arrives is: \[ P(1.5 < x < 3.9) = \]
- e. The probability that it will take longer than 1 second for the wave to crash onto the beach after a person arrives is: \[ P(x \geq 1) = \]

3. **Quartile Analysis**
- f. Find the maximum for the lower quartile: **\[ Q_1 = \]** seconds.

**Visual Aids:**

- The graph depicts a uniform distribution ranging from 0 to 4.5 seconds.
- A horizontal axis represents time in seconds, while the vertical axis represents the probability density function.
- Various intervals of interest (like point probability, specific intervals, and quartile information) are marked on the graph.

**Formulas to Utilize:**

For a uniform distribution \( U(a, b) \):
- Mean \( \mu = \frac{a + b}{2} \)
- Standard deviation \( \sigma = \frac{(b - a)}{\sqrt{12}} \)
- Probability for a range \( P(c < X < d) = \frac{d-c}{b-a} \)

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