Homework 5

Suppose you are waiting at the checkout line at the grocery store and estimate that, on average, 2 customers check out every 5 minutes. What is the probability that the next customer finishes checking out within the next 3 minutes?

Suppose you receive an average of 18 emails per day. What is the probability that your next email is received over 3 hours from now?

Suppose the average wait time at the DMV is 2 hours. If the wait time is exponentially distributed, what is the probability you are done in more than 30 but less than 75 minutes?

In a certain town, the number of 911 calls each day is Poisson distributed with mean 76.4. What is the value of the parameter lambda for this Poisson distribution?

Suppose the number of house fires each month is Poisson distributed with mean 25. What is the probability that exactly 27 fires occur next month?

Suppose the number of students that fail out of a particular school each year is Poisson distributed with mean 2.6. What is the probability that the number of students who fail out next year is less than 2.6?

If X is N(0,1) what is the probability that X is less than 1.12?

If X is N(0,3) what is the probability that X is less than 1.12?

If the average price of oranges is $1 with a variance of $0.25, what is the probability that a random selection of 80 oranges from 80 (independent) stores has an average price of over $1.06?

If a lumber company supplies an average of 10 tons of lumber per order with a variance of 9, what is the probability that the total tonnage of lumber sold over the next 196 orders is under 1900 tons? Assume each order is independent of each other order.