SOLUTION: The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/25 where x goes between 4 and 29 minutes. Round answers to 4 decimal places when possi

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Question 1200058: The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/25 where x goes between 4 and 29 minutes. Round answers to 4 decimal places when possible.

a. This is a
Uniform
Correct distribution.
b. It is a
Continuous
Correct distribution.
c. The mean of this distribution is
16.5
Correct
d. The standard deviation is
7.2169
Correct
e. Find the probability that the time will be at most 12 minutes.
0.32
Correct
f. Find the probability that the time will be between 5 and 9 minutes.
0.16
Correct
g. Find the 41st percentile.
14.25
Correct
h. Find the probability that the time is more than 23 minutes given (or knowing that) it is at least 8 minutes.
0.2857
Incorrect
0.7143
I only need help for letter H. The answer for letter H is 0.7143 but I need help understanding how they got the answer.
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Your answer is right for part h.

P(greater than 23, given that it is at least 8) = (29-23)/(29-8) = 6/21 = 2/7 = .2857 (rounded)

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Part H

The gap from 23 to 29 is 6 units
The gap from 8 to 29 is 21 units
6/21 = 0.2857 approximately is the probability of being to the right of 23, given we automatically know we're to the right of 8.

The answer to part H should be 0.2857

It's curious how your teacher got 0.7143

My guess is that s/he mistakenly did 1-0.2857 = 0.7143
Or perhaps your teacher meant to ask "Find the probability that the time is less than 23 minutes given (or knowing that) it is at least 8 minutes."