1. The number of movies released in the past few years by studio and by genre is listed in the following table.

	Action	Adventure	Drama	Comedy	Thriller	Other
23	12	28	19	32	18	52
Warner Bros	14	9	16	12	10	26
20 Century Fox	34	6	25	32	37	18
Sony Pictures	27	17	34	26	22	16
Universal	21	28	12	14	31	29
Other	56	102	137	64	44	98

Suppose a recently released movie is selected at random. When necessary, round probabilities to 4 decimal places.

a) What is the probability that the movie is a thriller? Show your work.

b) What is the probability that the movie is from Sony Pictures or Universal? Show your work.

c) Suppose the movie is a drama. What is the probability that it is from 20th Century Fox? Show your work.

d) Suppose the movie chosen is from Warner Bros. What is the probability that it is an action, comedy, or thriller? Show your work.

e) Is the event "movie is an adventure" independent from "movie is from 20th Century Fox"? Show your work and explain.

2. In a 100 gram bag of pistachios, some shells are too difficult to open by hand. Let be the number of pistachios in a randomly selected bag that cannot be opened by hand. The probability distribution is given.

x	0	1	2	3	4	5
P(x)	0.45	0.275	0.125	0.085	0.05	0.015

a) Verify this is a valid probability distribution. Explain.

b) Find the mean and standard deviation for , rounded to 1 decimal place, and with applicable units. Show your work. Interpret the mean.

c) Find the probability that at least 2 pistachios in a bag cannot be opened by hand.

d) Suppose 3 bags of pistachios are selected at random. What is the probability that all 3 bags will have at least 4 pistachios that are too difficult to open by hand? Express your answer with 4 decimal places.

3. From a survey, it was found 38.6% of students taking a first-year statistics class have high math anxiety. Let be the number of students who have high math anxiety.

a) A random sample of 9 students taking first-year statistics is chosen and the number of students with high math anxiety is recorded. Explain why this is a binomial experiment.

b) In a random sample of 9 students taking first-year statistics, what is the probability that at least 2 students have high math anxiety? Show your work.

c) To check this claim, a random sample of 180 students taking a first-year statistics class is obtained. Find the mean and standard deviation for , rounded to 1 decimal place, and with applicable units. Show your work. Interpret the mean.

d) In a random sample of 180 students taking first-year statistics, would it be unusual to have 85 students with high math anxiety? Explain and justify your procedure. (Hint: Check that it is appropriate to use the Empirical Rule.)

e) Based on your conclusion from part d), is there reason to suggest that the claim, "38.6% of students in a first-year statistics class have high math anxiety" is false? Explain.

4. Your friend is never on time and is regularly anywhere from 2 to 18 minutes late. Let represent the length of time in minutes that they are late and assume it has a uniform distribution.

a) Draw the probability density of .

b) You and your friend are going to an 8:20 PM movie. They agreed to pick you up from your house at 7:45 PM (...but you know they will be late!). It takes 21 minutes to drive to the theatre from your house, and an additional 8 minutes to buy tickets and snacks. What is the probability that you will be seated before the movie begins? Use a labelled probability density diagram and proper probability notation as part of your solution.