📌🔁🎯Statistical Reasoning_IA 3 Review #1

A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3

• For three rolls of the die, a number less than 3 will land face up one time

• It will take three rolls of the die before a number less than 3 lands face up for the first time

Matteo plays on his school basketball team. From past history, he knows that his probability of making a basket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimate the probability of making at least 3 baskets on his next 5 free throw attempts. Which of the following assignments of the digits 0 to 9 could be used for the simulation?

• Let the even digits represent making a basket and the odd digits represent not making a basket

• Let the digits 0 and 1 represent making a basket and the digits from 2 to 9 represent not making a basket

• Let the digits from 0 to 3 represent making a basket and the digits from 4 to 9 represent not making a basket

• Let the digits from 0 to 6 represent making a basket and the digits from 7 to 9 represent not making a basket

• Let the digits from 0 to 7 represent making a basket and the digits 8 and 9 represent not making a basket

An online customer service department estimates that about 15 percent of callers will have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram. Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?

• 0.150

• 0.190

• 0.474

• 0.526

• 0.810

The seniors at three high schools were surveyed about their plans after graduation. One senior from the high schools will be selected at random. What is the probability that the senior selected will not be from High School B given that the senior responded with a choice other than college?

A student is applying to two different agencies for scholarships. Based on the student's academic record, the probability that the student will be awarded a scholarship from Agency A is 0.55 and the probability that the student will be awarded a scholarship from Agency B is 0.40. Furthermore, if the student is awarded a scholarship from Agency A, the probability that the student will be awarded a scholarship from Agency B is 0.60. What is the probability that the student will be awarded at least one of the two scholarships?

• 0.60

• 0.62

• 0.71

• 0.73

• 0.95

The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?

• 0

• 1.00

• 1.79

• 3.50

• 28

In which of the following should the random variable X not be modeled with a geometric distribution?

• According to a recent study, approximately 8% of adults in the country have a master's degree. Let X represent the number of randomly selected adults in the country surveyed to find someone with a master’s degree.

• Suppose it is known that 5% of the light bulbs manufactured at a particular company are defective. Let X represent the number of randomly selected light bulbs that are inspected to find one defective light bulb.

• A particular basketball player is known to consistently make 90% of her free throws, and the outcomes of her free-throw attempts are independent. Let X represent the number of attempted free-throws to get one missed free-throw.

• In a bag of 30 different colored candies, about 20% are red. One candy will be selected one at a time without replacement, and its color will be recorded. Let X represent the number of candies selected before red is selected.

• It is believed that about 40% of people in the country have purchased a certain product. Let X represent the number of people randomly selected to find the first one who has purchased the product.

The following histogram shows the ages, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?

• The mean and the median are equal in value because the distribution is symmetric.

• The mean is most likely less than the median because the distribution is skewed to the right.

• The mean is most likely less than the median because the distribution is skewed to the left.

• The mean is most likely greater than the median because the distribution is skewed to the right.

• The mean is most likely greater than the median because the distribution is skewed to the left.

The following histogram summarizes the amount spent on plane tickets to travel home, in dollars, for a group of 30 college students. If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram?

• The heights of the bars

• The widths of the bars

• The number of bars

• The sum of the frequencies

• The shape of the distribution

A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?

• 0.59 months per pound

• 0.59 pounds per month

• 0.59

• 0.59 months times pounds

• 0.59 month pounds