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.

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.

  1. The mean of this distribution is 
  2. The standard deviation is 
  3. The probability that wave will crash onto the beach exactly 3.2 seconds after the person arrives is P(x = 3.2) = 
  4. 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) = 
  5. 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) = 
  6. Find the maximum for the lower quartile.  seconds.
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Expert Answer

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:

1
S(X-х)-
b-а
1
5.6 0
1
5.6
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1 S(X-х)- b-а 1 5.6 0 1 5.6

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Step 2

1)

The mean of the distribution is obtained as follows:

a+b
μ=
2
0+5.6
-2.8
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a+b μ= 2 0+5.6 -2.8

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Step 3

2)

The standard deviation of the distrib...

b-a
/12
5.6-0
v12
1.6166
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b-a /12 5.6-0 v12 1.6166

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