Question

Today, the waves are crashing onto the beach every 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 6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 3.3 seconds after the person arrives is P(x = 3.3) = d. The probability that the wave will crash onto the beach between 1.4 and 4 seconds after the person arrives is P(1.4 < x < 4) = e. The probability that it will take longer than 2.1 seconds for the wave to crash onto the beach after the person arrives is P(x > 2.1) = f. Suppose that the person has already been standing at the shoreline for 0.2 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 4.6 seconds for the wave to crash onto the shoreline. g. 93% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the minimum for the lower quartile. seconds.

Answer 1

The PDF of is

a) The mean of Uniform distribution is

b) The standard deviation is

c) The point probability of continuous distribution is 0. So

d) The probability,

e) The probability,