Company Inc owns a DC in Maryland with disruptions the year due to snowstorms. The number of disruptions follows a Poisson distribution with an average of 8.8 disruptions per year.

1. What is the probability that the number of disruptions next year at this DC is equal to or less than 4?

2. What is the probability of facing no disruptions at this DC during next year?

The time to recover from a disruption follows a uniform distribution with a minimum of 4 and a maximum of 13 days.

3. If a disruption happens, what is the average time the DC will be closed for?

4. If a disruption happens, what is the probability that the DC will be closed for more than 7 days?

1. An American Medical Association study showed 20% of all Americans suffer from high blood pressure. Suppose we randomly sample ten Americans to determine the number in the sample who have high blood pressure.

1. What is the probability at most two persons have high blood pressure? _____

2. What is the probability exactly five persons have high blood pressure? _____

3. What is the probability between two and six persons, inclusive, have high blood pressure? ______

4. What is the variance of the number of persons who have high blood pressure (in random samples of ten individuals)? _______

Two students take the same test which consists of 5 questions, each one with 5 answers, each one with only 1 correct answer. If the students respond the test randomly

i) What is the probability that both of the students get the same number of correct answers?

ii) Find the probability that both tests are the same (assume that each test is independent from each other)

iii) What is the expected number of correct answers for each student?

iv) What is the probability that both students pass the test if they have to get at least 3 correct answers to pass it?

Two coins are tossed at the same time. Let random variable be the number of heads showing.

a) Construct a probability distribution for

b) Find the expected value of the number of heads.

Two fair coins are flipped at the same time.

1) What is the probability of getting a match (same face on both coins)? Answer for part 1 [The answer should be a number rounded to five decimal places, don't use symbols such as %]

2) What is the probability of getting at least two heads? Answer for part 2 [The answer should be a number rounded to five decimal places, don't use symbols such as %]

It is estimated that 27% of births at a particular hospital are by caesarian section. Suppose a sample of 5 births is taken from this hospital.

(a). What is the probability that at most 2 births will be by caesarian section in this hospital?



(b). Write the R code to compute the probability in part (a).



(c). What is the mean number of births delivered by caesarian section in this hospital?



(d). What is the standard deviation of the number births delivered by caesarian section in this hospital?

A child counts the number of cracks in the sidewalk along the block she lives in (about 1/8 mile of sidewalk). Suppose the expected number of cracks in a block of sidewalk is 2.

a) Which distribution would be best to use to model this situation? Explain.

b) What is the probability that she observes three or more cracks?

c) What is the probability that she observed exactly two cracks in 1/2 of the block?

An average of 0.8 accident occur per day in a particular large city. Let x be the number of accidents per day. What is the probability, rounded to the nearest 4 decimal places, that no accident will occur in this city on a given day?

What is the probability, rounded to the nearest 4 decimal places, that one or two accidents will occur in this city on a given day?

A really bad carton of 18 eggs contains 7 spoiled eggs. An unsuspecting chef picks 4 eggs at random for this "Mega-Omelet Surprise". Let x be the number of unspoiled eggs in a sample of 4 eggs. Find the probability that the number of unspoiled eggs among the 4 selected is at least 1. Round your answer to the nearest 4 decimal places.

What are all the possible values that x can assume.

Overall, the amount of work-hours involved in the festival preparation is normally distributed around 50 hours with a standard deviation of 6 hours.

a) What’s the probability that the mean number of work-hours will be between 20 and 30?

b) The members at or below the 15%ile of number of worked-hours must attend a one-on-one meeting with their supervisor. At least how many work-hours you should have in order to avoid attending such session?

c) How likely (what is the probability) is it to have the number of involved work-hours below 50?

d) How likely (what is the probability) is it that some employee will have his/her involved work-hours between 48 and 53?

e) Compute the upper 10%ile.

(Please type answers if possible--handwriting is hard to read)