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Quantitative Reasoning Final Exam (100% Correct)
Questions and Answers (Latest Update)
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 6. If you get a 66 on the exam, your standard score (z-score) is
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
Suppose you again carry out a test of the hypothesis describes in question 8, but this time your results show that prices are above the national average, and by an amount that you might find by chance in only 1 out of 100 similar tests. A good description of this result would be that you've found a result that is statistically significant at the 0.01 level Suppose you toss a coin three times. In terms of the number of heads, which of the following outcomes represents the same event as an outcome of tails, heads, tails (THT)? TTH During the course of the basketball season, Lisa made 80 out of 100 free throws. When we say that her probability of making a free throw is 0.8, what type of probability are we stating? a relative frequency probability A box contains 20 fruits, but only 4 of them are oranges. When we say that the probability of drawing one of the oranges at random is 0.2, what type of probability are we stating? a theoretical probability Suppose the probability of winning a certain prize in the lottery is 0.001. What is the probability of not winning? 1 - 0. When you toss one fair coin, the probability of heads is 1/2. Assuming all the coins are fair, this means that if you toss 1000 coins, the number of heads will be close to, but not necessarily exactly, 500
On a roll of two dice, Serena bets that the sum will be 6, and Mackenzie bets that the sum will be 9. Who has a higher probability of winning the bet? Serena 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
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 expected value when it sells policies, what is the minimum that the company must charge for five insurance policies in this subdivision? $2000 per year We have an expert-written solution to this problem!
You know a shortcut to work that uses side streets instead of the freeway. Most of the time, the shortcut takes 5 minutes off the driving time by freeway. However, about once in every ten trips, an accident blocks traffic on the shortcut, with the result that the trip takes 20 minutes longer than it would by freeway. In terms of the amount of time the shortcut saves, what is the expected value of the shortcut? (5 minutes x 0.9) + (-20 minutes x 0.1) Cameron is betting on a game in which the probability of winning is 1 in 4. He's lost ten games in a row, so he decides to double his bet on the eleventh game. This strategy shows poor logic, as he has a 75% chance of losing the double bet Cameron is betting on a game in which the probability of winning is 1 in 4. He's won ten games in a row, so he decides to double his bet on the eleventh game. This strategy shows poor logic, as he has a 75% chance of losing the double bet A $1 slot machine at a casino is set so that it returns 97% of all the money put into it in the form of winnings, with most of the winnings in the form of huge but low-probability jackpots. What is your probability of winning when you put $1 in this slot machine? it cannot be calculated from the given data, but it is certainly quite low Consider the slot machine described in Question 9. Which statement is true if patrons have put $ million into this slot machine? the casino's profit has been close to $300, Given almost 40,000 annual fatalities due to car crashes in the United States, the average number of Americans killed in car crashes each day is approximately 100
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 5 x4x3x2x 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.
