Two events are mutually exclusive if they cannot occur simultaneously in agiven probability experiment.

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Question 2 (1 point)

If an experiment has two classifications of outcome, then each outcome has a probability of .

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Question 3 (1 point)

The central limit theorem assures us that a population is normally distributed provided that it has more than 30 individuals.

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Question 4 (1 point)

The probability of an event can exceed one if the event happens relatively often compared to other potential events of the experiment.

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Question 5 (1 point)

The complement of more than 5 successes is less than 5 successes."

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Question 6 (1 point)

S = {AAA, AAB, ABA, BAA, BBA, BAB, ABB, BBB} is a sample space comprised of eight equally likely outcomes of a probability experiment.

Find the probability that a randomly selected outcome has exactly two Bs.

Question 6 options:

0

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Question 7 (1 point)

S = {AAA, AAB, ABA, BAA, BBA, BAB, ABB, BBB} is a sample space comprised of eight equally likely outcomes of a probability experiment.

Find the probability that a randomly selected event has less than two As.

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Question 8 (1 point)

S = {AAA, AAB, ABA, BAA, BBA, BAB, ABB, BBB} is a sample space comprised of eight equally likely outcomes of a probability experiment.

Find the probability that a randomly selected outcome has at least one B.

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Question 9 (6 points)

A poker player must make a decision whether to call a bet or fold her hand. If she bets and wins, she will profit $200. If she bets and loses, she will lose $30. If she bets, the probability that she wins is 9/46, and the probability that she loses is 37/46. Find the expected value for this situation. Round to the nearest cent.

Question 9 options:

E=200*9/46+(-30)(37/46)=1800-1110/46=690/46=$15

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Question 10 (2 points)

Refer to the previous problem. If this poker player made that same bet many times in similar situations, would she expect to win or lose money over the long run? Your response should be based on the expected value.

Question 10 options:

She would win over the long run because the expected value is positive

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Question 11 (8 points)

A university will only accept students who score in the top 20% of all college bound students who take the ACT. If ACT scores for a particular year are normally distributed with a mean of 22.2 and a standard deviation of 5.6, what score would a student taking the ACT that year need to achieve to be eligible for acceptance to this school? Round to the nearest whole number. To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 12 (8 points)

A poker player tracks his profit per night. He notices that his profits can be modeled well by a normal distribution with a mean of $350 and a standard deviation of $625. Using this normal model, find the probability that this player wins more than $1000 on a randomly selected night.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 13 (8 points)

In the U.S., the average monthly mortgage payment (including principal and interest) is $982 with a standard deviation of $180. If the mortgage payments are normally distributed, find the probability that a randomly selected payment is between $1000 and $1200.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 14 (8 points)

Approximately 10% of American high school students drop out before graduation. Suppose 20 students are selected at random. Find the probability that all 20 of the selected students stayed in school and graduated.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 15 (8 points)

It is estimated that 15% of the homeowners in a small city pay for lawn care. Suppose 10 residents are selected at random. Find the probability that at least four of the selected homeowners pay for lawn care.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 16 (2 points)

A resale shop specializes in used DVDs. Historically, 5% of the DVDs they have sold to their customers are returned as unplayable. If a customer comes and buys 80 DVDs, how many should the store expect to be returned as unplayable? (This is the mean of a binomial random variable).

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Question 17 (8 points)

In a 2012 Gallup poll, 7% of Americans identified themselves as either vegetarian or vegan. Suppose 50 Americans are selected at random. What is the probability that fewer than than three of them would identify themselves as vegetarian or vegan?To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 18 (8 points)

A machine is designed to fill jars with spaghetti sauce. The amount of sauce it dispenses into the jars is normally distributed with a mean of 850 grams and a standard deviation of 8 grams. Suppose 16 jars are selected at random. Find the probability that the mean amount of sauce in these 16 jars is less than 845 grams.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 19 (8 points)

A club in a tourist area hands out 200 passes to their "invite only" VIP lounge. The lounge can only handle a total of 50 customers, but the owners know that historically 80% of the tourists who receive the passes will not show up. Find the probability that the number of people who try to redeem their passes exceeds the capacity of the VIP lounge.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 20 (8 points)

Full-time Ph.D. students receive an average of $13,000 per year. If the salaries are normally distributed with a standard deviation of $1500 per year, find the probability that a randomly selected Ph.D. student makes more than $10,000 per year.To receive full credit, you must show your workusing the correct input for one of our calculator functions.

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Question 21 (2 points)

Extra Credit Problem #1:

In a certain town in Illinois, it rained on 148 out of the 366 days in the year 2012. 22 of those days were Wednesdays, and 20 of those days were Saturdays. Suppose it was raining at noon on a Wednesday. What is the probability that it was sunny 60 hours later? In order to receive credit, you must supply a correct explanation for your answer.

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Question 22 (1 point)

Extra Credit Problem #2:

All contestants on a game show are given the choice of three doors: Behind one door is $1,000,000; behind the others, goats. The contestant picks a door, andthe host, who knows what's behind the doors, opens another door, revealing a goat. He then gives the contestant the option to switch to the remaining closed door or stick with his/her original choice. And guess what? You've just been selected to play! You choose a door and the host reveals a goat behind one of the other doors. Now he gives you the decision to stick or switch. You obviously want to give yourself the best chance of winning the cash (unless youre really, really into goats), so you nerd it up and contemplate which strategy would be best over the long run. You're such a dork....

Anyway, which of the following is true for contestants over the long run?

Question 22 options:

You have a better chance of winning the money if you switch to the other door.

You have a better chance of winning the money if you stick with your original choice

The probability of winning the money is the same (50%) whether you stick with your original choice or switch to the other door.

You arereally, really into goats, to the point where you'd choose one over a million bucks and intentionally get an extra credit question wrong by choosing this option.

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