Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 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 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in? seconds. Find the minimum for the upper quartile. seconds.

Question
Asked Oct 4, 2019

Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 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 1.4 seconds after the person arrives is P(x = 1.4) =
The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) =
The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) =
Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline.
84% of the time a person will wait at least how long before the wave crashes in? seconds.
Find the minimum for the upper quartile. seconds.

check_circleExpert Solution
Step 1

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

Consider, X be the random variable which represents the time from when a person arrives the shoreline until a crashing wave is observed. It follows uniform distribution with the parameters a= 0 and b = 5.1 seconds, that is,

XU(a,b)
xU(0,5.1)
The density function of X is,
1
fx (x)3.1-0
1
0<x5.1
5.1
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XU(a,b) xU(0,5.1) The density function of X is, 1 fx (x)3.1-0 1 0<x5.1 5.1

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Step 2

(a)

The mean of the distribution can be defined as :

Mean(uab
2
a+b
05.1
=
2
= 2.55
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Mean(uab 2 a+b 05.1 = 2 = 2.55

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Step 3

(b)

The standard deviation of the distri...

|(b-a)
Standard deviation (o):
12
|(5.1-0)
12
=1.4722
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|(b-a) Standard deviation (o): 12 |(5.1-0) 12 =1.4722

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