Stats Exam 3 Practice

In a certain country, the average age is 31 years old and the standard deviation is 4 years. If we select a simple random sample of 100 people from this country, what is the probability that the average age of our sample is at least 32?

0.006

A fair coin is tossed 10 times. If 𝑋 is the number of times that heads is tossed, what is 𝑃(3<𝑋≤6)?

0.65625

A box of writing utensils on a teacher's desk contains 5 red pencils, 7 green pencils, 9 red markers, and 4 green markers. What is the probability of selecting a red writing utensil or a marker?

18/25

Using a standard Normal table or technology, find the critical value 𝑧∗ for a 98% confidence level.

2.326

At a certain driver's license testing station, only 40% of all new drivers pass the behind‑the‑wheel test the first time they take it. A sample of 50 new drivers from a certain high school found that 36% of them had passed the test the first time. Which of these numbers is a parameter?

40%

To obtain a smaller margin of error:

choose a larger sample size.

For a simple random sample of size 𝑛n , the count 𝑋 of successes in the sample has a binomial distribution.

false

The probability of event 𝐴 is 𝑃(𝐴)=0.5, and the probability of event 𝐵 is 𝑃(𝐵)=0.7. Are 𝐴 and 𝐵 disjoint?

no

Choose the correct definition of a random variable from the list below. A random variable is

one whose values describe the outcome of some chance process.

The law of large numbers tells us that as sample size 𝑛 increases:

the sample mean approaches the population mean.

Suppose that 𝑋 is the count of successes in a binomial distribution with 𝑛n fixed observations and a probability 𝑝 of success on any given single observation. Let 𝑌 be the number of failures in the same 𝑛 observations. Will the binomial distribution for 𝑋 and 𝑌 necessarily have the same mean and/or standard deviation?

They will always have the same standard deviation, but they might not have the same mean.

A random variable 𝑥 has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a random sample of size 𝑛=36 and find a sample mean of 𝑥¯=98. What is a 95% confidence interval for the mean of 𝑥?

(94.08,101.92)

The random variable 𝑋X denotes the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. 𝑋 is known to have a Normal distribution, with a mean of 15 seconds and a standard deviation of 3 seconds. 𝑃(𝑋>20) has a rounded value of:

0.048.

The number of years of education of self‑employed individuals in the United States has a population mean of 13.6 years and a population standard deviation of 3 years. If we survey a random sample of 100 self‑employed people to determine the average number of years of education for the sample, what is the mean of the sampling distribution of 𝑥¯, the sample mean?

13.6 years

Students at University X must be in one of the following class ranks: freshman, sophomore, junior, or senior. At University X, 35% of the students are freshman and 30% are sophomores. If a student is selected at random, the probability that he or she is either a junior or a senior is:

35%.

At a certain driver's license testing station, only 40% of all new drivers pass the behind‑the‑wheel test the first time they take it. A sample of 50 new drivers from a certain high school found that 36% of them had passed the test the first time. Which of these numbers is a statistic?

36%

If we roll a single six‑sided die, the probability of rolling a 6 is 1/6. If we roll the die 60 times, how many times will we roll a 6?

It is impossible to determine from the information given.

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 80 mg/mi and standard deviation 6 mg/mi. A company has 16 cars of this model in its fleet. Using Table A, find the level 𝐿such that the probability that the average NOX + NMOG level 𝑥¯ for the fleet greater than 𝐿 is only 0.05?

L = 82.468

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋? Give reasons for your answer in each case. (c) Joe buys a ticket in his state's Pick 3 lottery game every week; 𝑋 is the number of times in a year that he wins a prize. Is it reasonable to use a binomial distribution for the random variable 𝑋? Select an answer choice.

Yes, a binomial distribution is reasonable.

When an opinion poll uses random digit dialing to select respondents for polls, the response rate (the percentage who actually provide a usable response to the poll) is approximately 10% for people contacted by cell phone. A pollster dials 20 cell phone numbers. 𝑋 is the number that respond to the pollster. Does 𝑋 have a binomial distribution?

Yes, the calls are independent, each one has two possibilities, and the probability of getting a usable response to the poll is the same for each call.

For which of the following situations would the central limit theorem not imply that the sample distribution for 𝑥¯ is approximately Normal?

a population is not Normal, and we use samples of size 𝑛=6.

A margin of error tells us:

how accurate the statistic is when using it to estimate the parameter.

Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter (k⁢g/m2) of fat‑free body mass. Typical young men have about 20 k⁢g/m2 . Each subject chose two images, one that represented his own level of body muscle and one that he thought represented "what women prefer." The mean gap between self‑image and "what women prefer" was 2.35 k⁢g/m2 . Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5 k⁢g/m2 . Give a 90% confidence interval for the mean amount of muscle young men think they should add to be attractive to women. (Enter your answers rounded to four decimal places.)

lower limit = 2.059 upper limit = 2.6408

According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic black females was 78.1 years. Assume that the standard deviation was 15 years, as suggested by the Bureau of Economic Research. The distribution of age at death, 𝑋, is not normal because it is skewed to the left. Nevertheless, the distribution of the mean, x¯, in all possible samples of size 𝑛n is approximately normal if 𝑛 is large enough, by the central limit theorem. Let x¯ be the mean life expectancy in a sample of 100 non‑Hispanic black females. Determine the interval centered at the population mean 𝜇 such that 95% of sample means x¯ will fall in the interval. Give your answers precise to one decimal.

lower limit: 75.2 years upper limit: 81.0 years

A surplus store gives a scratch‑off ticket to 2000 customers as they leave with their groceries. Can we expect these customers' average winnings to be close to the average winnings for the entire population of the scratch‑off ticket holders?

yes

The number of years of education of self‑employed individuals in the United States has a population mean of 13.6 years and a population standard deviation of 3 years. If we survey a random sample of 100 self‑employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of 𝑥¯, the sample mean?

0.3 years

Suppose we have a loaded die that gives the outcomes 1 through 6 according to the following probability distribution. Die outcome: 1, 2, 3, 4, 5, 6 Probability: 0.10, 0.20, 0.30, 0.2, ?, 0.1 What is the probability of rolling a 5?

1/10

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the chance you don't get an apple?

38/44

A box at a miniature golf course contains contains 44 red golf balls, 88 green golf balls, and 77 yellow golf balls. What is the probability of taking out a golf ball and having it be a red or a yellow golf ball? Express your answer as a percentage and round it to two decimal places.

Probability: 57.89

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋? Give reasons for your answer in each case. (b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult population of a large city. Each person in the pool is asked whether he or she opposes the death penalty; 𝑋 is the number who say "Yes." Is it reasonable to use a binomial distribution for the random variable 𝑋? Select an answer choice.

Yes, a binomial distribution is reasonable.

To obtain a smaller margin of error:

choose a smaller confidence level.

Personal probabilities are not important since they are based on personal judgment.

false

The random digits generated by a computer program are randomly generated.

false

The population distribution is_____ the sample ______ and the population standard deviation is _____. Therefore, ______ to find a 90% z-confidence interval.

normal, size is irrelevant, known, yes all the requirements are met

I select two cards from a standard deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space 𝑆 for the possible outcomes?

𝑆={(red, red), (red, black), (black, red), (black, black)}

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the sample space for your action?

𝑆={apple, orange, banana, pear, peach, plum, mango}

A random variable 𝑋 can take on the value 0, 1, 2, or 3. Which of the following is a possible probability model for 𝑋?

𝑋: 0, 1, 2, 3 𝑃(𝑋): 0.5, 0.3, 0.1, 0.1

Suppose there are three cards in a deck: one marked with a "1,"one marked with a "2,"and one marked with a "5." You draw two cards at random, without replacement from the deck of three cards. The sample space 𝑆={(1,2), (2,1),(1,5),(5,1),(2,5),(5,2)} consists of these six equally likely outcomes. Let 𝑋 be the total of the two cards drawn. Which of the following is the correct set of probabilities for 𝑋?

𝑋: 3, 6, 7 P: 1/3, 1/3, 1/3,

The 2015 American Time Use survey contains data on how many minutes of sleep per night each of 10,900 survey participants estimated they get. The times follow the Normal distribution with mean 529.9 minutes and standard deviation 135.6 minutes. An SRS of 100 of the participants has a mean time of 𝑥¯=514.4 minutes. A second SRS of size 100 has mean 𝑥¯=539.3 minutes. After many SRSs, the values of the sample mean 𝑥¯ follow the Normal distribution with mean 529.9 minutes and standard deviation 13.56 minutes. (a) What is the population? What values does the population distribution describe? What is this distribution? (b) What values does the sampling distribution of 𝑥¯ describe? What is the sampling distribution?

(a) The population is the 10,900 respondents to the American Time Use Survey. - The population distribution describes the minutes of sleep per night for the individuals in this population. This distribution is Normal with mean 529.9 minutes and standard deviation 135.6 minutes. (b) The sampling distribution describes the distribution of the average sleep time for 100 randomly selected individuals from this population. This distribution is Normal with mean 529.9 minutes and standard deviation 13.56 minutes.

Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell‑checking software will catch nonword errors but not word errors. Human proofreaders catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. (a) If the student matches the usual 70% rate, what is the distribution of the number of errors caught? -If the student matches the usual 70% rate, what is the distribution of the number of errors missed? (b) Missing 3 or more out of 10 errors seems a poor performance. What is the probability that a proofreader who catches 70% of word errors misses exactly 3 out of 10? - What is the probability that a proofreader who catches 70% of word errors misses 3 or more out of 10? Use software.

(a) binomial, with n=10 and p=0.7 - binomial, with n=10 and 𝑝=0.3 (b) 0.2668 - 0.6172

In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 84 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 78 mg/mi and standard deviation 6 mg/mi. (a) What is the probability that a single car of this model emits more than 84 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 36 cars of this model in its fleet. What is the probability that the average NOX + NMOG level 𝑥¯ of these cars is above 84 mg/mi? (Enter your answer rounded to four decimal places.)

(a) probability: 0.1587 (b) probability: 0

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score 𝜇μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.8. Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495. In answering the questions, use z‑scores rounded to two decimal places. (a) If you choose one student at random, what is the probability that the student's score is between 490 and 500? Use Table A, or software to calculate your answer. (Enter your answer rounded to four decimal places.) (b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score 𝑥¯? (Enter your answer rounded to two decimal places.) (c) What is the probability that the mean score of your sample is between 490 and 500? (Enter your answer rounded to four decimal places.)

(a) probability: 0.3616 (b) standard deviation: 1.80 (c) probability: 0.9946

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot. In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was 𝑥¯=282. We want to estimate the mean score 𝜇μ in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation 𝜎=110. (a) If we take many samples, the sample mean 𝑥¯varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score 𝜇μ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.) (b) According to the 95 part of the 68‑95‑99.7 rule, 95% of all values of 𝑥¯fall within how many points on either side of the unknown mean 𝜇μ ? (Enter your answer rounded to four decimal places.) (c) What is the 95% confidence interval for the population mean score 𝜇μ based on this one sample? (Enter your answer rounded to one decimal place.)

(a) standard deviation = 0.2973 (b) points = 0.5946 (c) lower value = 281.4; higher value = 282.6

To estimate the mean score 𝜇μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.5. You want your sample mean 𝑥¯ to estimate 𝜇μ with an error of no more than 0.9 point in either direction. (a) What standard deviation must 𝑥¯ have so that 99.7% of all samples give an 𝑥¯ within 0.9 point of 𝜇μ ? Use the 68-95-99.7 rule. (Enter your answer rounded to four decimal places.) (b) How large an SRS do you need in order to reduce the standard deviation of 𝑥¯ to the value you found? (Enter your answer rounded to the nearest whole number.)

(a) standard deviation of 𝑥¯= 0.30 (b) SRS size = 469

A government sample survey plans to measure the total cholesterol level of an SRS of men aged 20-34. Suppose that, in fact, the total cholesterol level of all men aged 20-34 follows the Normal distribution with mean 𝜇=182 milligrams per deciliter (mg/dL) and standard deviation 𝜎=37 mg/dL. Use Table A to answer the questions, where necessary. (a) Choose an SRS of 1000 men from this population. What is the sampling distribution of 𝑥¯? (Use the units of mg/dL.) What is the probability that 𝑥¯ takes a value between 180 and 184 mg/dL? This is the probability that 𝑥¯ estimates 𝜇μ within ±2 mg/dL. (b) Choose an SRS of 1000 men from this population. Now what is the probability that 𝑥¯ falls within ±2 mg/dL of 𝜇μ ? (Enter your answer rounded to three decimal places.)

(a) the 𝑁(182,3.7) distribution - 0.4108 (b) probability: 0.912

A sales representative makes visits to customers. Based on his history, the probability that he makes a sale on any visit is 0.15. It is reasonable to assume that customers' decisions are independent of one another. If the sales representative makes 10 visits in a day, what is the chance he makes at least five sales?

0.0099

There are five multiple choice questions on an exam, each having responses a, b, c, and d. Each question is worth 5 points, and only one option per question is correct. Suppose the student guesses the answer to each question, and these guesses, from question to question, are independent. If the student needs at least 20 points to pass the test, the probability that the student passes is closest to:

0.0156

A carpet manufacturer is inspecting for flaws in the finished product. If there are too many blemishes, the carpet will have to be destroyed. He finds the number of flaws in each square yard and is interested in the average number of flaws per 10 square yards of material. If we assume the standard deviation of the number of flaws per square yard is 0.6, the sample mean, 𝑥¯, for the 10 square yards will have what standard deviation? Round the answer to the nearest hundredth.

0.19

Suppose that 𝑥 is a Normally distributed random variable with an unknown mean 𝜇μ and known standard deviation 6. If we take repeated samples of size 100 and compute the sample means x¯, 95% of all of these values of 𝑥¯should lie within a distance of _ from 𝜇μ . (Use the 68‑95‑99.7 rule.)

1.2

There are five multiple choice questions on an exam, each having responses a, b, c, and d. Each question is worth 5 points, and only one option per question is correct. Suppose the student guesses the answer to each question, and these guesses, from question to question, are independent. The student's mean number of questions correct on the exam should be:

1.25

Imagine that a traffic intersection has a stop light that repeatedly cycles through the normal sequence of traffic signals (green light, yellow light, and red light). In each cycle the stop light is green for 30 s, yellow for 3 s, and red for 50 s. Assume that cars arrive at the intersection uniformly, which means that in any one interval of time, approximately the same number of cars arrive at the intersection at any other time interval of equal length. Determine the probability that a car arrives at the intersection while the stop light is yellow. Give your answer as a percentage precise to two decimal places.

3.61%

Suppose that we compute a 90% 𝑧 confidence interval for an unknown population mean 𝜇μ . Which of the following is a correct interpretation?

90% of all possible 𝑧 confidence intervals computed from samples of the same size would contain 𝜇

Suppose that we compute a 90% 𝑧 confidence interval for an unknown population mean 𝜇μ . Which of the following is a correct interpretation?

90% of all possible 𝑧 confidence intervals computed from samples of the same size would contain 𝜇μ .

A student is chosen at random from a statistics class. Which of the following events are disjoint?

Event 𝐴 is that the student is a junior. Event 𝐵 is that the student is a senior.

Statisticians prefer large samples. Select the correct explanation of the effect of increasing the size of a sample on the margin of error of a 95% confidence interval.

Regardless of the level of confidence (the 95% confidence level has nothing to do with it), larger samples reduce margins of error, which provides greater precision in estimating 𝜇μ .

Ramon is interested in whether the global rise in temperature is also showing up locally in his town, Centerdale. He plans to look up the average annual temperature for Centerdale for five recent randomly selected years. He wants to report the number of years whose temperature was higher than the previous year's temperature. What is the random variable in Ramon's study, and what are its possible values?

The random variable is the number of years in which the temperature increased from the previous year. Its possible values are {0,1,2,3,4,5}.

A researcher is planning to construct a one-sample 𝑧‑confidence interval for a population mean 𝜇.μ. Select the statements that would lead to a smaller margin of error, assuming the other factors remain the same.

The researcher increases the sample size. The population standard deviation turns out to be lower than expected. The researcher lowers the confidence level.

A researcher is planning to construct a one-sample z‑confidence interval for a population mean 𝜇.μ. Select the statements that would lead to a smaller margin of error, assuming the other factors remain the same.

The researcher lowers the confidence level. The population standard deviation turns out to be lower than expected. The researcher increases the sample size.

Mark all of the following requirements that have been met with yes, and all the requirements that have not been met with no.

The sample is a simple random sample: NO The population standard deviation is known: YES The population from which the data are obtained is normally distributed, or the sample size is large enough: YES The requirements for constructing a z-confidence interval for a mean have been met: NO

Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 transactions at random, she found that the average amount spent was $32.15. She then computed a 90% confidence interval to be between $29.18 and $35.12. Which statement gives a valid interpretation of the interval?

The store manager is 90% confident that the average amount spent by all customers is between $29.18 and $35.12.

In the following hypothetical scenarios, classify each of the specified number as a parameter or a statistic.

There are nine justices currently serving in the United States Supreme Court, and 44% of them were appointed after the year 2000. The 44% here is a: PARAMETER In 1936, Literary Digest polled 2.3 million adults in the United States, and 57% of them said they would vote for Alf Landon for the Presidency. The 57% here is a: STATISTIC The survey results from 12 local parks show the mean height of 60 ft for mature oak trees. The mean height of 60 ft is a: STATISTIC The 59 players on the roster of a championship football team have a mean weight of 248.6 pounds with a standard deviation of 44.6 pounds. The 44.6 pounds is a: PARAMETER In a random sample of homeowners in the United States, it is found that 34% of the sampled homeowners renew their home warranty. The 34% here is a: STATISTIC There have been 44 Presidents of the United States, and 36% of them were Democrats. The 36% here is a: PARAMETER In a 2015 Gallup poll of 1025 adults living in the United States, 53% said they trust the judicial branch of the federal government. The 53% here is a: STATISTIC The 72 employees at ABC company have a mean income of $52,317 with a standard deviation of $36,829. The $36,829 is a: PARAMETER In a random sample of households in the United States, it is found that 51% of the sampled households have at least one high‑definition television. The 51% here is a: STATISTIC

Choose the correct definition of a sampling distribution. The sampling distribution of a statistic of size 𝑛 is

the distribution of all values of the statistic resulting from all samples of size 𝑛 taken from the same population.

Choose the correct definition of a sampling distribution. The sampling distribution of a statistic of size 𝑛n is

the distribution of all values of the statistic resulting from all samples of size 𝑛n taken from the same population.

The binomial coefficient, written (𝑛𝑘)(nk) =𝑛!𝑘!(𝑛−𝑘!)=n!k!(n−k!) , gives what information?

the number of ways in which 𝑘 successes in 𝑛 trials can be obtained

The probability distribution of a random variable is:

the possible values of the random variable and the frequency with which the variable takes each value.

Determine the margin of error, 𝑚m, of a 95% confidence interval for the mean IQ score of all students with the disorder. Assume that the standard deviation IQ score among the population of all students with the disorder is the same as the standard deviation of IQ score for the general population, 𝜎=15 points. Give your answer precise to at least two decimal places

𝑚= 7.35 points

Which of the following values of 𝑛n and 𝑝 would give a binomial distribution for which we should avoid using the Normal approximation?

𝑛=30, 𝑝=0.8

STATE: How heavy a load (in pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Given are data from students doing a laboratory exercise. We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume that characteristics of materials vary Normally. Suppose that the strength of pieces of wood like these follows a Normal distribution with a standard deviation of 3000 pounds. PLAN: We will estimate 𝜇μ by giving a 99% confidence interval. SOLVE: Find the sample mean 𝑥¯. (Enter your answer rounded to the nearest whole number.) Give a 99% confidence interval, [𝑙𝑜𝑤,ℎ𝑖𝑔ℎ][l⁢o⁢w,h⁢i⁢g⁢h], for the mean load required to pull the wood apart. (Enter your answers rounded to the nearest whole number.)

𝑥¯= 30841 low = 29114 high = 32568

Let 𝑋 be a binominal random variable with 𝑛=9 and 𝑝=0.2. What is the probability of four successes; that is, 𝑃(𝑋=4)?

0.066

In a certain high school, 20% of the graduating seniors have chosen to attend The Ohio State University. If there are 265 seniors in the graduating class, the number who will go to The Ohio State University is a binominal random variable. What is the standard deviation of the number of students who will attend Ohio State?

6.51

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋? Give reasons for your answer in each case. An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the count 𝑋 finish defects (dimples, ripples, etc.) in the car's paint. Is it reasonable to use a binomial distribution for the random variable 𝑋?

A binomial distribution is not reasonable because 𝑛n is not fixed. A binomial distribution is not reasonable because trials are not independent and 𝑝 is likely not constant. A binomial distribution is not reasonable because there are more than two outcomes of interest.

Which of the following would have a binomial distribution?

A fair coin is tossed 10 times. 𝑋 is the number of heads tossed in these 10 flips.

The probability of event 𝐴 is 𝑃(𝐴)=0.3, and the probability of event 𝐵 is 𝑃(𝐵)=0.25. Are 𝐴 and 𝐵 disjoint?

It is impossible to determine from the information given.

A set of four cards consists of two red cards and two black cards. The cards are shuffled thoroughly and I am dealt two cards. I found the number of red cards (𝑋) in these two cards. The random variable 𝑋 has which of the given probability distributions?

Neither answer option is correct.

A student reads that a recent poll finds a 95%95% confidence interval for the mean ideal weight given by adult American women is 139±1.3 pounds. Asked to explain the meaning of the confidence interval for mean ideal weight, the student answers: "We can be 95% confident that future samples of adult American women will say that their mean ideal weight is between 137.7 and 140.3 pounds."

No. If we repeated the sample over and over, 95% of all future sample means would be within 1.96 standard deviations of 𝜇μ , the true, unknown value of the mean ideal weight for American women. Future samples will not depend on the results of a previous sample.

Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

No. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means.

Boxes of 6-inch slate flooring tile contain 40 tiles per box. The count 𝑋 is the number of cracked tiles in a box. You have noticed that most boxes contain no cracked tiles, but if there are cracked tiles in a box, then there are usually several. Does 𝑋 have a binomial distribution?

No. The trials are not independent. If one tile in a box is cracked, there are likely more tiles cracked.

The figure displays several possible finite probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not valid. That is, they do not obey the rules. Which are valid and which are not? Select the best answer, with the correct explanation of what is wrong in the case of the invalid models.

Only Model 2 is valid. Models 1, 3, and 4 have probabilities that do not sum to 1. Model 4 has some probabilities that are greater than 1.

Suppose a weather forecast reports that the probability of snow this week is 0.35. The forecast states that if it snows this week, the probability that it snows next week is 0.42. If it does not snow this week, the probability that it snows next week is 0.25. The tree diagram depicts the possible weather event outcomes with the associated probabilities. What is the probability that it will snow next week? Provide your answer with precision to two decimal places.

P(snow next week) = 0.31

Suppose that fish inhabiting the river in the town of Glenmeadow have a 30% rate of parasite incidence. Carl is a fisherman who wants to verify the parasite infection rate of Glenmeadow's fish. He catches 1000 fish at random and sequentially tests them for parasites. Assuming that the true parasite incidence rate is 30%, which of the following statements is the most accurate?

The more fish Carl tests, the more likely he is to find a 30% parasite incidence rate.

In the 2000 presidential election, three candidates split the vote as follows. Bush 47.9% Gore 48.4% Nader 2.7% We will consider a vote for Al Gore a "success." We can look back and select a random sample of 50 voters from the 2000 election, and count the number of those who voted for Gore. Suppose, in that sample, that 23 of the 50 (46%) voted for Gore. Which of the following is correct?

The numbers 23 and 0.46 are statistics, and the number 0.484 is a parameter.

The Department of Motor Vehicles reports that 32% of all vehicles registered in a state are made by a Japanese or a European automaker. The number 32% is best described as:

a parameter

A confidence interval is constructed to estimate the value of:

a parameter.

As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. If 𝑋 is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample, then 𝑋 has approximately:

an 𝑁(20,4) distribution.

STATE: How heavy a load (in pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Given are data from students doing a laboratory exercise. 33,19033,19031,86031,86032,59032,59026,52026,52033,28033,28032,32032,32033,02033,02032,03032,03030,46030,46032,70032,70023,04023,04030,93030,93032,72032,72033,65033,65032,34032,34024,05024,05030,17030,17031,30031,30028,73028,73031,92031,920 We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume that characteristics of materials vary Normally. Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds. PLAN: We will estimate 𝜇μ by giving a 95% confidence interval. SOLVE: Find the sample mean 𝑥¯. (Enter your answer rounded to the nearest whole number.) Give a 95% confidence interval,[low,high], for the mean load required to pull the wood apart. (Enter your answers rounded to the nearest whole number.)

𝑥¯= 30841 low = 29526 high = 32156

The critical value 𝑧∗ for confidence level 75% is not in table c. Use Table A of standard Normal probabilities to find 𝑧∗. Select the correct critical value. Select the plot that correctly shows the critical value and the area left in each tail when the central area matches the confidence level of 75%.

𝑧∗=1.15 Graph with 0.125 on sides and -1.15 and 1.15 on x-axis

Consider the following probability distribution for a random variable 𝑋:3, 4, 5, 6, 7 𝑃(𝑋): 0.15, 0.10, 0.20, 0.25, 0.30 What is 𝑃(𝑋≤5.5)?

0.45

Of the 132 patients that visited Doctor McClary's office this week, 30 described themselves as former smokers, 𝐹, and 22 described themselves as current smokers, 𝐶. (a) How many patients were current or former smokers, |C∪F|? (b) What is the probability that a randomly-selected patient is a current or former smoker, P(C∪F)? Express your answer to three decimal places.

(a) |C∪F|= 52 (b) 𝑃(𝐶∪𝐹)= 0.394

As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. If 𝑋 is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample, then the probability that fewer than 30 buy a packet after tasting a free sample is approximately:

0.9938

A simple random sample is drawn from a large population with a Normal distribution. What is the sampling distribution of the sample mean?

𝑁(𝜇,𝜎𝑛√)