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Ch. 5 SRIS Practice Test

Last updated about 3 years ago
40 questions
For any decimals on this test, round to 2 decimal places.
In 2017, quarterback Alex Smith had the highest statistical passer rating of any quarterback in the NFL. The two-way table summarizes the association between the quarter of the game and outcome of his pass attempts. Suppose we select one pass attempt at random.
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What is the probability that the pass attempt was in the first quarter?

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What is the probability that the pass attempt was after the first quarter?

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What is the probability that the pass attempt was in the first quarter and complete?

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What is the probability that the pass attempt was in the first quarter or complete?

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What is the probability that the pass attempt was in the first quarter, given that it was complete?

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What is the probability that the pass attempt was complete, given that it was in the first quarter?

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What is the probability that the pass attempt was complete, given that it was after the first quarter?

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Let event A be “Attempt was in the first quarter” and event B be “Attempt was complete.” Explain what it means to say that events A and B are independent.

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Based on your previous answers, are the events “Attempt was in the first quarter” and
“Attempt was complete“ independent? Prove mathematically.

You can type or use the "show your work" space to draw your answer.

Many baseball pitchers can throw 3 different types of pitches: fastball, curve, and change-up. When facing a batter with only one strike left, a certain pitcher throws his fastball 45% of the time, curveball 35% of the time, and change-up the remaining times. The pitcher gets the batter out 75% of the time when he throws a fastball, 80% of the time when he throws a curveball, and 65% of the time when he throws a change-up. Randomly select one batter during a game.

Fill out the probabilities on the tree diagram. Then calculate the probabilities of each of the 6 possible outcomes. Enter each probability as a decimal (not a percent).
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Calculate the probability that the batter is not out.

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Given that the batter was out, what is the probability that the pitcher threw a fastball?

Suppose that on 4th down a football team has the ball on their opponent’s 45-yard line with 2 yards to go for a first down. They are losing by 1 point and there are 15 minutes remaining in the game. The coach is considering whether to punt or go for the first down. If the coach decides to punt, they have a win probability of 0.44. If they go for it and are successful, their win probability goes up to 0.56. However, if they go for it and fail, their win probability goes down to 0.38.

Label the following tree diagram. Assume that the team has a 0.50 probability of successfully gaining the 2 yards to make a new first down if they go for it.
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Interpret the value 0.44 in the context of this question

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Use the tree diagram to calculate the probability that the team wins the game by attempting to go for the first down.

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Given this information, is attempting to go for it a good strategy? Explain your reasoning.

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How high does the probability of making the first down need to be in order to make this a good strategy? Use p for the probability for a successful first down instead of 0.50. For what values of p would it be worthwhile to attempt to go for it in this context?