Question

Asked Nov 2, 2019

Today, the waves are crashing onto the beach every 5.3 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.3 seconds. Round to 4 decimal places where possible.

The probability that the wave will crash onto the beach between 0.4 and 4.7 seconds after the person arrives is P(0.4 < *x* < 4.7) =

The probability that it will take longer than 2.96 seconds for the wave to crash onto the beach after the person arrives is P(*x* ≥≥ 2.96) =

Find the maximum for the lower quartile. seconds.

Step 1

Let X be the random variable uniformly distributed between 0 and 5.3 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:

Step 2

The probability that the wave will crash on to the beach between 0.4 and 4.7 seconds after the person arrives is calculated as follows:

Step 3

The probability that it will take longer than 2.96 seconds for the wave to cr...

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