Question

Asked Nov 18, 2019

Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible.

- The mean of this distribution is
- The standard deviation is
- The probability that wave will crash onto the beach exactly 3.2 seconds after the person arrives is P(
*x*= 3.2) = - The probability that the wave will crash onto the beach between 0.9 and 3.8 seconds after the person arrives is P(0.9 <
*x*< 3.8) = - The probability that it will take longer than 3.12 seconds for the wave to crash onto the beach after the person arrives is P(
*x*≥≥ 3.12) = - Find the maximum for the lower quartile. seconds.

Step 1

Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are solving the first 3 parts for you, according to our policy. If you need help with any of the other parts, please re-post the question and mention the part you want answered.

Let X be random variable uniformly distributed between 0 and 5.6 seconds.

Denote X as the time from a person arrives at the shoreline until a crashing wave is observed.

Thus, the probability density function of X is shown below:

Step 2

1)

The mean of the distribution is obtained as follows:

Step 3

2)

The standard deviation of the distrib...

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