Introduction to Statistics and Probability (MATH-037)

Question 1.

The table below shows the Greeks status and response to the question "have your ever violated the honor code?" for 41 random student who filled out our opening week survey.

	Violated code	Never violated code
Greek	5	5
Non-Greek	12	22

a) What is the probability that a randomly selected student from this group is Greek and has

violated the honor code?

b) What is the probability that a randomly selected student from this group is Greek or has

violated the code?

c) What is the probability that a randomly selected student from this group is Greek give they are someone who has violated the honor code?

d) What is the probability that a randomly selected student from the group has violated the honor code given they are Greek?

e)Briefly explain why c and d are so different

Question 2

Suppose that the chance of getting an ultra-rare LOL doll in a surprise bubble are 5%.

Pearl buys two LOL surprise bubbles

a) What is the probability distribution from the number of ultra-rare dolls she will get?

b) What is the probability she gets at least one ultra-rare doll?

Question 3

A pekka is a type of troop in clash of clans that never seems to go in the direction I want them to go. Suppose that in an attack, a pekka has a 60% chance of turning right when it reaches a wall and a 40% chance of turning left. If it turns right, it will destroy 15 buildings, but if it turns left, it will only destroy 10. What are the expected value and standard deviation of the number of building it will destroy in a random attack?

Question 4

For many viruses, the distribution of number of days until it reaches a peak number of infections is often modelled with a normal distribution. Suppose that for one particular type of virus, the expected number of days until it peaks is 60 days with a standard deviation of 7 days.

a) What is the probability that this virus will take less than 50 days to peak?

b) Ted is planning a vacation and want to make sure there is a 90% chance that the virus will have peaked before he leaves. What is the minimum amount of days he should wait to leave? Hint: What is the 90^th percentile of peak times?

Question 5

Suppose now that we look at 16 independent outbreaks of the virus from the last problem and calculate the sample mean of the peak times.

a) What is the expected value of the sample mean?

b) What is the standard error of the sample mean?

c) What are the cutoffs for the middle 90% of the sample mean distribution?