Question
In: Statistics and Probability
A company services copiers. A review of its records shows that the time taken for a...
A company services copiers. A review of its records shows that the time taken for a service call is a normally distributed random variable with a mean of 150 minutes and a standard deviation of 40 minutes.
a. What proportion of service calls takes less than 2 hours?
b. What proportion of service calls takes between 120 and 180 minutes?
c. Find the 99% quantile of the distribution and interpret the result.
d. Suppose that the times of the subsequent service calls are independent. Find the 99% quantile of the distribution of the overall time taken for two consecutive service calls and interpret the result.
Solutions
Expert Solution
a)
2 hours = 2*60 = 120 minutes
b)
c)
Answer: 243.20 minutes
d)
Let T shows the total time taken by two consecutive calls call X1 and X2. Given that
Since X1 and X2 are normally distributed so T will also normally distributed with following parameters
So required 99 quantile will be
Answer: 431.80 minutes
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