I have been working at this one for a while and it's time to enlist some help.
The question is as follows.
"The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time in uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be
a. less than 70 minutes?
b. between 65 and 70 minutes?
c. greater than 65 minutes?
d. What are the mean and standard deviation of the commuting time?"
I am lost on how to even really start this problem because of the scheduled time and actual times being different. Any help in how to solve this problem would be greatly appreciated. Answers are nice but I am aiming more for the "how" to solve this.
The question is as follows.
"The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time in uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be
a. less than 70 minutes?
b. between 65 and 70 minutes?
c. greater than 65 minutes?
d. What are the mean and standard deviation of the commuting time?"
I am lost on how to even really start this problem because of the scheduled time and actual times being different. Any help in how to solve this problem would be greatly appreciated. Answers are nice but I am aiming more for the "how" to solve this.
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The scheduled time does not matter. You are only asked questions about the actual times.
64-------------70-------74
The prob less than 70 is
(7 0-64)/(74-64) = 6/10 = 0.6
b. (70-65) / (74-64) = 5/10 = 0.5
c. (74-65) / (74-64) = 9/10 = 0.9
d. Mean is 64 + (74-64)/2 = 69
Now use the definition of standard deviation to find it for this distribution.
You should get (74-64)/sqrt(12)
64-------------70-------74
The prob less than 70 is
(7 0-64)/(74-64) = 6/10 = 0.6
b. (70-65) / (74-64) = 5/10 = 0.5
c. (74-65) / (74-64) = 9/10 = 0.9
d. Mean is 64 + (74-64)/2 = 69
Now use the definition of standard deviation to find it for this distribution.
You should get (74-64)/sqrt(12)