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Answer:
a)
b)
Step-by-step explanation:
Part a
Let A the random variable that represent "The arrival time (minutes) for a daily flight from Boston to New York ". And we know that the distribution of A is given by:
We select our starting point a=0 representing 9:05 AM and the amount of minutes between 9:05 am to 9:55 am are 50 ans for this reason b =50
For ths uniform distribution the expected value is given by where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:
And the variance is given by:
And the standard deviation by definition is just the square root of the variance:
Part b
If we convert 9:30 AM to our scale we know that we have 25 minutes between 9:05 AM and 9:30 AM.
For this case we want to find this probability:
And we can find this probability using the complement rule like this:
And we can use the cumulative distribution function given by:
And we got: