AP Stats Multiple Choice Final

The overall shape of this distribution is...

clearly skewed to the left

In order to use the formula σ of p hat = sqrt((p(1-p)/n) to calculate the standard deviation of the sampling n distribution of the sample population, which of the following conditions must be met? I. np > or equal to 10 and n-np > or equal to 10 II. The population's distribution is approximately Normal. III. The sample size is less that 10% of the population size.

III only

In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct?

If a sample of 1000 trees was examined, the variation of the sample proportion would be smaller than in a sample of 100 trees.

The five-number summary for a data set is given by min = 5, Q1= 18, median = 20, Q3= 40, max = 75. If you wanted to construct a boxplot for the data set (that is, one that would show outliers, if any existed), what would be the maximum possible length of the right-side "whisker"?

33

The mean body temperature for humans is taken to be 98.6 F with a standard deviation of 0.62 F. Given that C=5/9 (F -32), What are the mean and standard deviation measured in Celsius?

37 and 0.33

Suppose we roll a fair die four times. The probability that a 6 occurs on exactly one of the rolls is...

4(1/6)^1(5/6)^3

The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults who report drinking alcohol occasionally. About what percent of these adults consume between 4 and 8 ounces per week?

40%

In a large population of adults, the proportion who own a horse is 12%. Suppose 200 adults are randomly selected for a market research campaign about horse care products. The sampling distribution of the sample proportion of horse owner is...

approximately Normal, mean 0.12, standard deviation 0.023.

You need to randomly choose a number from 1 to 9. What is the probability that you choose the number 7.5?

0.0000 --> infinite numbers so that number is very specific

In the Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: ... The probability that a randomly-selected household has at least two cell phones is...

.80

A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to make $20,000 profit. If it is cool that day, she expects to make a $5,000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records, the weather office has estimated the chances of a warm day to be .60; the chances of a cold day to be .25. What is the producer's expected profit?

$11,450

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket: Amount Won: $500 $100 $25 $0 Probability: 0.01 0.05 0.20 0.74 Which of the following are the mean and standard deviation, respectively, of the winnings?

$15.00, $53.85

Suppose that you have torn a tendon and are fac- ing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together 1% of the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?

.8660

AP 2.2 add up first four probabilities

.9375

AP2.18-don't count 116 twice

(a)

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which fewer than 65 own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

(c)

Which of the following histograms could have been constructed from the same set of data summarized by the box plot above?

(d) - looks like/has similar shape to the box plot

Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown the X is approximately Normally distributed with a mean of 250 pounds and a standard deviation of 50 pounds. What is P(x>326 pounds)?

0.0668 --> normalcdf(325, 1E99, 250, 50)

You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red?

0.1551

Julie and Devon are applying for summer jobs at a local restaurant. After interviewing them, the restaurant owner says, "The probability that I hire Julie is 0.7, and the probability that I hire Devon is 0.4. The probability that I hire one or the other of you is 0.9." What is the probability that both Julie and Devon get hired?

0.20 --> solve for unknown variable in given equation.

A randomly selected student is asked to respond Yes, No, or Maybe to the question "Do you intend to vote in the next presidential election?" The sample space is {Yes, No, Maybe}. Which of the following represents a legitimate assignment of probabilities for this sample space?

0.4, 0.4, 0.2 --> prob. must add up to one

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?

0.526

According to the DuPont 2007 Global Automotive Color Popularity Report, 19% of all cars manufactured in 2007 were white. In a random sample of 100 cars parked in long-term parking at Philadelphia International Airport, 22% of the cars were white. Which of the following statements is true?

19% is a parameter, 22% is a statistic.

You record the age, marital status, and earned income of a sample of 1463 women. The number of variables you have recorded is...

2 quantitative, 1 categorical

The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min=12, Q1=15, Median=16, Q3=18, Max=24. Which of the following statements is true?

24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

3.02 - adding standard deviations

The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects that a certain number of the bags will be under filled, so the company will replace for free the 5% of bags that have too few briquets. What is the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free?

418 (invNorm (.05, 450, 20))

Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability of being correct is 0.98, let two digits simulate one word; 00-97 mean "correct." The program recognizes words (or not) independently. To stimulate the program's performance on 10 words, use these random digits: 60970 70024 17868 29843 61790 90656 87964 The number of words recognized correctly out of ten is...

9

Which of the following best describes a sampling distribution?

A probability distribution that describes the relative likelihood of all possible values of a statistic.

Select a random integer from -100 to 100. Which of the following events are mutually exclusive?

A: the number is above 50; B: the number is less than 20.

Suppose you are sampling from a distribution that is strongly skewed left. Which of the following statements about the sampling distribution of the sample mean is true?

As the sample size increases, the shape of the sampling distribution gets closer to a Normal distribution. ("n" increases making the variability less).

Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?

At least 50% of the scores in section 3 are higher than all of the scores in section 1.

Date were collected on the amount, in dollars, that the individual customers spent on dinner in an Italian restaurant. The quartiles for these data are given below. Which of the following statements must be true for these customers?

At least half of the customers spent less than or equal to $44.27 and at least half spent greater than or equal to $44.27.

George has an average bowling score of 180 and bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. Bill has an average bowling score of 190 and bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in his own league, George or Bill?

Bill, because his standardized score is higher than George's.

In order for the random variable X to have geometric distribution, which of the following conditions must X satisfy? I. p=0.5 II. The number of trials is fixed. III. Trials are independent. IV. The probability of success has to be the same for each trial.

III and IV

Which of following statements are true when taking a simple random sample from a large population? (assume 10% rule) I. The sampling distribution of X bar has a standard deviation of (std. dev./ sqrt(n)) even if the population is not Normally distributed. II. The sampling distribution of X bar is Normal if the population has a Normal distribution. III. When n is large, the sampling distribution of X bar is approximately Normal even if the population is not Normally distributed.

I, II, and III

Heights, in inches, for the 200 graduating seniors from Washington High School are summarized in the frequency table below. Which of the following statements about the median height is true

It is greater than or equal to 60 inches but less than 66 inches.

Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?

It means that your grade is 2 standard deviations above the mean for this exam.

Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?

It means that your grade is two standard deviation above the mean for this exam.

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. A cumulative relative frequency graph is shown below from data collected over the past year. According to the graph, the shortest 80% of calls will take how long to complete?

Less than 10 minutes

A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following:

One digit from the random digit table simulates one answer, with 0 or 1 = right and all other digits = wrong. Ten digits from the table simulate 10 answers.

Based on the shape of this distribution, what measures of center and spread would be most appropriate to report?

The median and the interquartile range

A basketball team with 11 players of differing heights trades its shortest player to another team for a tall center who is now the tallest player on the team. Which one of the following statements is FALSE?

The median height will remain the same.

The probability of any outcome of a random phenomenon is...

The proportion of times the outcome occurs in a very long series of repetitions.

A graph not shown of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

In a certain large population of adults, the distribution of IQ scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. The distribution of the sample mean of IQ scores is

approximately Normal with mean 122 and standard deviation 0.35.

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of A, given B is

is 1/6.

The mean of this distribution (don't try to fine it) will be...

less than the median

A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every hour a sample of 18 chips is selected at random for testing and the number of chips that meet the specifications is recorded. What is the approximate mean and standard deviation of the number of chips meeting specifications?

mew= 16.2; σ=1.273

A census of the labor force in a large metropolitan area found that the time it takes for people to commute to work has a mean of 20.5 minutes and standard deviation of 15.4 minutes. Assuming that the people chose are independent, what is the correct way to compute the probability that a random sample of 40 people have a mean commute time that is greater than 25 minutes?

normalcdf(25, 1E99, 20.5, 2.43)

The variance of sum of two random variables X and Y is...

σx^2 + σy^2 only if X and Y are independent.