A)While testing a building's fire alarms, the probability that any fire alarm will fail is 0.01....

A)While testing a building's fire alarms, the probability that any fire alarm will fail is 0.01. Suppose a building has 10 fire alarms, all which are independent of one another. The test will be passed if all fire alarms work.

a) 5 buildings are tested on the same day and each building has 10 fire alarms. How likely is it that 4 or more buildings pass the test? ( A building will pass if all 10 fire alarms are good)

B) Customers arrive at a restaurant according to a Poisson process at a rate of 30 customers per hour. There is a probability of 0.8 that a customer will dine in.

b) Say the customers are arriving independently of one another. What is the probability that 30 customers will arrive in a 1 hour time period AND all 30 will dine in?

C) Suppose a phd applicant is either accepted to a graduate program or not. if accepted the student can choose to attend or not attend. Suppose a graduate program has sent acceptance letters to 50 applicatns, but only had enough funding for 30 students. Let the students who were accepted to the program be independent of one another and the chance that a student will join the program be 0.6.

c) what is the probability that the graduate program will have enough funding for all students that joins the program.

Expert Solution

Solution: Here concept of binomial probability law is used.

milcah answered 2 months ago

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