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Quantitative Reasoning Final Exam
Graphs of normal distributions - always have the same characteristic bell shape In a normal distribution, the mean - is equal to the median In a normal distribution, data values farther from the mean are - less common than data values close to the mean Consider wages at a fast food restaurant where most of the workers earn the minimum wage. Would you expect the wages of all workers at this restaurant to have a normal distribution? - no, because a normal distribution is symmetric, but no one earns less than the minimum wage In a normal distribution, about two-thirds of the data values fall within - 1 standard deviation of the mean Suppose a car driven under different conditions gets a mean gas mileage of 40 miles per gallon with a standard deviation of 3 miles per gallon. If you drive this car many times, the gas mileage on 95% of the trips will be between - 34 and 46 miles per gallon Consider again the car described in question 6. On about what percentage of the trips will the gas mileage be less than 37 miles per gallon? - 16% Consider an exam with a normal distribution of scores with a mean of 75 and a standard deviation of
- If you get a 66 on the exam, your standard score (z-score) is - -1. A friend tells you that his IQ is in the 102nd percentile. You can conclude that -
he doesn't understand percentiles Researchers are testing a new cancer treatment. To determine whether the treatment offers a statistically significant improvement in survival rates, the researchers must - compare the survival rate with the new treatment to that with other treatments or no treatment Working with equal sample sizes, researchers compared three new cold remedies to a placebo. Which remedy is most likely to be most effective? - the one that gave results statistically significant at the 0.01 level Researchers conduct 20 different experiments to test the effectiveness of a new weight loss pill compared to the effectiveness of a placebo. For 19 of the 20 experiments, the results are not statistically significant. However, one of the experiments shows that the pill works better than the placebo with statistical significance at the 0.05 level. A fair report of the combined results from all 20 experiments would say that - there is no evidence that the treatment works A poll finds that 35% of the people surveyed approve of the President's handling of the economy, with a margin of error (for 95% confidence) of 3%. The 95% confidence interval for this poll is - 32% to 38% Suppose the poll described in question 5 were repeated one month later (with a new sample) and 33% of the people surveyed approve of the President's handling of the economy. Which is the correct conclusion about the percentage of the population that approves of the President's handling of the economy? - the two polls results do not differ enough to allow us to draw a conclusion about any change Consider a survey with a margin of error of 4%. If you want to reduce the margin of error to 2%, you should repeat the survey with - four times as many people You want to test your hypothesis that local gas stations are charging much more than the national average price for gasoline. A good null hypothesis for this test would be - local gas prices equal the national average gas price
Suppose you toss four 6-sided dice. How many outcomes are possible? - 6x6x6x Suppose you toss three 6-sided dice. How many different sums are possible? - 16 You are playing five-card poker with a deck of 52 cards. If you make a probability distribution showing the individual probabilities of all possible hands, the sum of the individual probabilities will be - 1 The odds on (or odds against) TripleTreat winning the Kentucky Derby are 4 to 1. This means that whoever set the odds thinks that TripleTreat's probability of winning is - 1 in 5, or 1/ The probability of rolling two dice and getting a double 6 is 1 in 36. Suppose you roll two dice twice. Which statement is not true? - the probability of getting a double 6 on at least one of the two rolls is 2/ The rule P(A and B) = P(A) x P(B) holds - only if an outcome of A on one trial does not affect the probability of an outcome of B on the next In which of the following cases are the events dependent? - the probability of selecting a red M&M from a bag, eating it, and then selecting another red M&M A box of candy contains five dark chocolates and five white chocolates. If you pick randomly and eat each candy after choosing it, what is the probability of choosing three dark chocolates in a row? - 1/2 x 4/9 x 3/ The events of being born on a Monday and being born in June are - overlapping
You toss two coins 10 times, and you want to know the probability of getting two heads at least once in the 10 trials. To get the answer in the easiest possible way, what is the first thing you should calculate? - the probability of not getting two heads in a single trial You purchase 10 lottery tickets for which the probability of winning some prize on a single ticket is 1 in 50 (or 0.02). Your probability of having at least one winner among your 10 ticket is - 1-0.98^ One in 10 people on campus has blonde hair. In 20 random encounters, what is the probability of meeting at least one blonde-haired person? - 1-0.9^ Suppose that the probability of a hurricane striking Florida in any single year is 1 in 10 and that this probability has been the same for the pat 100 years. Which of the following is implied by the law of large numbers? - Florida has been hit by close to (but not necessarily exactly) 10 hurricanes in the past 100 years Consider a lottery with 100 million tickets in which each ticket has a unique number. Each ticket sold for $1, and one ticket is drawn for a single prize of $75 million (and no other prizes). The expected value of a single ticket is - -$0. Consider the lottery described in Question 2. If you were to spend $1 million to purchase 1 million lottery tickets, the most likely result would be that - you would lose your entire $1 million You are betting on a game in which each bet has an expected value of -$0.40. This means that - if you play the game many times, on average you will lose about $0.40 per game An insurance company knows that the average cost to build a home in a new California subdivision is $100,000 and that in any particular year there is a 1 in 50 chance of a wildfire destroying all the homes in the subdivision. Based on these data and assuming the insurance company wants a positive
Which statement about life expectancy is true? - it decreases as you get older The life expectancy at birth of an American girl today is about 81 years. Does this mean that we should expect girls born today to live an average of 81 years? - no, because this life expectancy assumes no change in medical science or public health, both of which are almost certain to change If life expectancies continued to rise as they did in the 20th century, how would the increase affect current projections about the future of Social Security? - it would mean current projections underestimate how much Social Security will pay in benefits You are asked to create a 5-character password, and each character may be any of the 26 letters of the alphabet or the 10 numerals 0 through 9. How many different passwords are possible? - 36^ A waitress has four different entrees for the four people sitting at a table, but has forgotten which person ordered which entree. In how many different ways could she serve the entrees? - 24 A teacher has 28 students, and 5 of them will be chosen to participate in a play that has 5 distinct roles. Which of the following questions requires calculating permutations? - once the 5 children have been chosen, how many different ways can their roles be arranged? The number of permutations of 12 objects grouped 5 at a time is written - 12 P 5 A soccer coach has a team of 15 children and 7 of the children are on the field at one time. Which number is largest? - the number of permutations of 7 children that can be chosen from the 15
One term in the denominator of the combinations formula is (n-r)!. Suppose you are trying to determine the number of different possible 4-person teams that can be put together from a group of 9 people. In this case, the term (n-r)! means - 5x4x3x2x The number of different 4-person teams (order does not matter) that can be put together from a group of 9 people is - 9x8x7x6 / 4x3x2x One person in a stadium filled with 100,000 people is chosen at random to win a free airline ticket. The probability that someone will win the ticket - is 1 One person in a stadium filled with 100,000 people is chosen at random to win a free pair of airline tickets. What is the probability that it will not be you? -
There are 365 possible birthdays in a year. In a class of 25 students, the chance of finding 2 students with the same birthday is - greater than 0.
