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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 work using 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 work using 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 work using 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 work using 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 work using 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 work using 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, and the host, who knows whats 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? Youve 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 you?re really, really into goats), so you nerd it up and contemplate which strategy would be best over the long run. Youre 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 are really, really into goats, to the point where youd choose one over a million bucks and intentionally get an extra credit question wrong by choosing this option.|
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