Question

Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 120 seconds. a. What is the probability that the time between the arrivals of two customers will be less than 69 seconds? b. What is the probability that the time between the arrivals of two customers will be between 20 and 102 seconds? c. What is the probability that the time between the arrivals of two customers will be greater than 39 seconds? d. What are the mean and standard deviation of the time between the arrival of two customers?

 a. The probability that the time between arrivals will be less than 69 seconds is (Round to four decimal places as needed.)

Answer 1

Solution:

X = Time between arrivals of customers at a bank during the noon to 1 pm hour has a Uniform distribution between 0 to 120 seconds.
That is X ~ Uniform( a= 0 , b = 120)

Part a) Find:

P( X <69 ) = .......?

We use cumulative distribution function of Uniform distribution:

.

Part b)

P(20 < X< 102)= ...........?

P(20 < X< 102)= P( X < 102 ) - P( X < 20)

Part c)  

P( X > 39) =...........?

P( X > 39) = 1 - P( X < 39)

Part d)

Mean:

Standard Deviation: