Question

Asked Nov 2, 2019

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Today, the waves are crashing onto the beach every 5.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.8 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 3.1 seconds after the person arrives is P(
*x*= 3.1) = - The probability that the wave will crash onto the beach between 0.9 and 3.4 seconds after the person arrives is P(0.9 <
*x*< 3.4) = - The probability that it will take longer than 1.96 seconds for the wave to crash onto the beach after the person arrives is P(
*x*≥≥ 1.96) = - Find the minimum for the upper quartile. seconds.

Step 1

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Step 2

The probability density function of a uniform distribution over the interval from ‘a’ and ‘b’ is defined below:

It is given that the time from when a person arrives at the shoreline until a crashing wave is observed follow a uniform distribution from 0 to 5.8 seconds.

Step 3

1.

The mean of the distribution can be obtained as shown below:

Therefore, the...

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