AP Statistics Unit 4 MCQ: Part A

A consumer group is investigating the number of flights at a certain airline that are overbooked. They conducted a simulation to estimate the probability of overbooked flights in the next 5 flights. The results of 1,000 trials are shown in the following histogram.

Based on the histogram, what is the probability that at least 4 of the next 5 flights at the airline will be overbooked?

• 0.114

• 0.332

• 0.446

• 0.500

• 0.886

Answer explanation

The sum of the relative frequencies of the bars for 4 and 5 is 0.446.

Consider rolling two number cubes, each of which has its faces numbered from 1 to 6. The cubes will be rolled and the sum of the numbers landing face up will be recorded. Let the event E represent the event of rolling a sum of 5. How many outcomes are in the collection for event E?

• One

• Two

• Four

• Five

• Six

Answer explanation

There are four outcomes that sum to 5: 1 and 4, 4 and 1, 2 and 3, 3 and 2.

In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population?

• Let the even digits represent birds with a wingspan greater than 10 inches and the odd digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits 0 and 1 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 2 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

Answer explanation

The four digits 0, 1, 2, and 3 represent 40% of the 10 digits and would model 40% of the population.

Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected?

• {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)}

• {(oatmeal, pancakes), (oatmeal, eggs), (eggs, pancakes), (coffee, tea)}

• {(coffee, tea, oatmeal), (coffee, tea, eggs), (coffee, tea, pancakes)}

• {oatmeal, coffee, pancakes, eggs, tea}

• {(oatmeal, eggs, pancakes), (coffee, tea)}

Answer explanation

There are three possible selections for a meal and two possible selections for a beverage, so there are 3×2=6 ways of pairing a meal with a beverage. The sample space is a set of all six possible outcomes of one meal with one beverage.

At Mike's favorite coffee shop, the coffee of the day is either a dark roast, a medium roast, or a light roast. From past experience, Mike knows that the probability of the coffee being a light roast is 0.15 and the probability of the coffee being a dark roast is 0.25. What is the probability of the coffee of the day not being a light roast or a dark roast on the next day that Mike visits the coffee shop?

• 0.15

• 0.25

• 0.40

• 0.60

• 0.85

Answer explanation

The event of the coffee not being a light roast or a dark roast is the complement of the event of the coffee being either a light roast or a dark roast, which is the same as the coffee being a medium roast (since there are only three options). The probability of the coffee being either a light roast or a dark roast is 0.25+0.15=0.40, so the probability of the complement is 1−0.40=0.60.

Amy has 12 brown golf tees, 8 white golf tees, 10 red golf tees, 6 blue golf tees, and 12 green golf tees in her golf bag. If she selects one of the tees from the bag at random, what is the probability that she selects a tee that is not brown or blue?

A business journal reports that the probability that Internet users in the United States will use a mobile payment app is 0.60. The journal claims this indicates that out of 5 randomly selected Internet users, 3 will use the mobile payment app.

Is the business journal interpreting the probability correctly?

• No, because the Internet users are not independent of each other.

• No, because only 60% of all people use the Internet.

• No, because 0.60 represents probability in the long run for many Internet users.

• Yes, because Internet users are selected at random.

• Yes, because 3 out of 5 is equal to 60%.

Answer explanation

When surveying many Internet users, the long-run relative frequency of using the mobile payment app is 0.60, or 3 out of 5. Such a ratio does not necessarily apply to a single observation of 5 Internet users.

A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.

Which of the following is the best interpretation of the probability 0.20 ?

• For all workers in the United States, 20% will work in finance.

• For all finance workers, 20% will have a tattoo.

• For all people with tattoos, 20% will work in finance.

• For a specific group of 5 finance workers, 1 will have a tattoo.

• For a specific group of 5 people with a tattoo, 1 will work in finance.

Answer explanation

In the long run, 0.20 is the relative frequency at which a finance worker will have a tattoo.

A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.

Which of the following is the best interpretation of the probability that one spin of the spinner will land in a shaded sector?

• For 6 spins, the spinner will land in a shaded sector 4 times.

• For 6 spins, the spinner will land in a shaded sector 2 times.

At a local elementary school, 35 percent of all students have brown eyes, 45 percent have brown hair, and 60 percent have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event that the selected person has brown eyes, and let H represent the event that the selected person has brown hair.

Are E and H mutually exclusive events?