Stats exam 3

Imagine that Alina's shower leaks and she calls the plumber. The plumber tells her that the problem is caused by either a leaky drain or a cracked shower pan, but never both. He also tells her that, in his experience, a leaky drain is the cause of the problem in about 90%90% of cases. If he discovers that the drain is the problem, he can fix it for $250$250. If he discovers that the shower pan is the problem, he must charge $2500$2500 instead. What is the expected value of the repair price? Please round your answer to the nearest whole dollar.

$475

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

(94.08,101.92)

Suppose that 𝑥x is a Normally distributed random variable with an unknown mean 𝜇μ and known standard deviation 6. If we take repeated samplesof size 100 and compute the sample means 𝑥¯x¯ , 95% of all of these values of 𝑥¯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

Suppose we have a loaded die that gives the outcomes 1 through 6 according to the following probability distribution. What is the probability of rolling a 5?

1/10

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¯x¯ , the sample mean?

13.6 years

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

2.326

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%

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

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%

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

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

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

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋?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 𝑋X 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 there are more than two outcomes of interest. A binomial distribution is not reasonable because 𝑛n is not fixed. A binomial distribution is not reasonable because trials are not independent and 𝑝p is likely not constant.

Which of the following would have a binomial distribution?

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

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 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

The random variable 𝑋 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)P(X>20) has a rounded value of:

0.048

Let 𝑋 be a binominal random variable with 𝑛=9and 𝑝=0 . What is the probability of four successes; that is, 𝑃(𝑋=4)?

0.066

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¯x¯ , for the 10 square yards will have what standard deviation? Round the answer to the nearest hundredth.

0.19

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%70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 1010 word errors. b) Missing 33 or more out of 10 errors10 errors seems a poor performance. What is the probability that a proofreader who catches 70%70% of word errors misses exactly 33 out of 10? What is the probability that a proofreader who catches 70%70% of word errors misses 33 or more out of 10?10? Use software.

0.2668 0.6172

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¯x¯ , the sample mean?

0.3 years

What is the probability that 𝑥¯x¯ takes a value between 180180 and 184184 mg/dL? This is the probability that 𝑥¯x¯ estimates 𝜇μ within ±2±2 mg/dL. (b) Choose an SRS of 10001000 men from this population. Now what is the probability that 𝑥¯x¯ falls within ±2±2 mg/dL of 𝜇μ ? (Enter your answer rounded to three decimal places.)

0.4108 b)probability: 0.912

Consider the following probability distribution for a random variable 𝑋: 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

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

As part of a promotion for a new type of cracker, free samples areoffered 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 𝑋X 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 student is chosen at random from a statistics class. Which of the following events are disjoint?

Event 𝐴A is that the student is a junior. Event 𝐵B is that the student is a senior.

If we roll a single six‑sided die, the probability of rolling a 6 is 1/6.1/6. 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 probability of event 𝐴A is 𝑃(𝐴)=0.3, and the probability of event 𝐵B is 𝑃(𝐵)=0.25. Are 𝐴A and 𝐵B 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)(X) in these two cards. The random variable 𝑋X 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±1.3139±1.3 pounds. Asked to explain the meaning of the confidence interval for mean ideal weight, the student answers: "We can be 95%95% confident that future samples of adult American women will say that their mean ideal weight is between 137.7137.7 and 140.3140.3 pounds." Is this explanation correct?

No. If we repeated the sample over and over, 95%95% of all future sample means would be within 1.961.96 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 𝑋Xhave 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 22 is valid. Models 1,1, 3,3, and 44 have probabilities that do not sum to 1.1. Model 44 has some probabilities that are greater than 1.

No. If we repeated the sample over and over, 95%95% of all future sample means would be within 1.961.96 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.

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

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.

You read online that the probability of being dealt four‑of‑a‑kind in a five‑card poker hand is 1/41651/4165 . Explain carefully what this means. In particular, explain why it does not mean that if you are dealt 41654165 five‑card poker hands, one will be four‑of‑a‑kind. Select the best explanation from the choices.

The probability is actually saying that in the long run, with a large number of five‑card poker hands, the fraction in which you will be dealt a four‑of‑a‑kind is 1/41651

Select all of the statements that are axioms of probability.

The probability of the sample space is 1 The probability of any event is between 0 and 1 inclusively. If two events 𝐴A and 𝐵B are mutually exclusive (disjoint), then 𝑃(𝐴 or 𝐵)=𝑃(𝐴)+𝑃(𝐵)

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 𝑧z‑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.

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 𝑛n 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.

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋?X? Give reasons for your answer in each case. (b) The pool of potential jurors for a murder case contains 100100 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; 𝑋X is the number who say "Yes." Is it reasonable to use a binomial distribution for the random variable 𝑋?X? Select an answer choice.

Yes, a binomial distribution is reasonable.

In each of the following situations, is it reasonable to use a binomial distribution for the random variable 𝑋?X? Give reasons for your answer in each case. (c) Joe buys a ticket in his state's Pick 33 lottery game every week; 𝑋X 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?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%10% for people contacted by cell phone. A pollster dials 2020 cell phone numbers. 𝑋X is the number that respond to the pollster. Does 𝑋X 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.

A confidence interval is constructed to estimate the value of:

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.

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

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

Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 2020 years and over at random. Define two events: 𝐴=A= the person chosen is obese 𝐵=B= the person chosen is overweight, but not obese According to the National Center for Health Statistics, 𝑃(𝐴)=0.38P⁡(A)=0.38 and 𝑃(𝐵)=0.33P⁡(B)=0.33 . (a) Select the correct explanation describing why events 𝐴A and 𝐵B are disjoint. (b) Select the correct description stating what the event 𝐴A or 𝐵B is. What is 𝑃(𝐴 or 𝐵)P⁡(A or B)? (c) If 𝐶C is the event that the person chosen has normal weight or less, what is 𝑃(𝐶)P⁡(C)

a) Event 𝐵B rules out obese subjects. b)𝐴 or 𝐵 is the event that the person is overweight or obese. 𝑃(𝐴 or 𝐵)=0.71 c)𝑃(𝐶)=0.29

The 2015 American Time Use survey contains data on how many minutes of sleep per night each of 10,90010,900 survey participants estimated they get. The times follow the Normal distribution with mean 529.9529.9 minutes and standard deviation 135.6135.6 minutes. An SRS of 100100 of the participants has a mean time of 𝑥¯=514.4x¯=514.4 minutes. A second SRS of size 100100 has mean 𝑥¯=539.3x¯=539.3 minutes. After many SRSs, the values of the sample mean 𝑥¯x¯ follow the Normal distribution with mean 529.9529.9 minutes and standard deviation 13.5613.56 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¯x¯ describe? What is the sampling distribution?

a)The population is the 10,90010,900 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 529.9529.9 minutes and standard deviation 135.6135.6 minutes. b)The sampling distribution describes the distribution of the average sleep time for 100100 randomly selected individuals from this population. This distribution is Normal with mean 529.9529.9 minutes and standard deviation 13.5613.56 minutes.

The 2015 American Time Use survey contains data on how many minutes of sleep per night each of 10,90010,900 survey participants estimated they get. The times follow the Normal distribution with mean 529.9529.9 minutes and standard deviation 135.6135.6 minutes. An SRS of 100100 of the participants has a mean time of 𝑥¯=514.4x¯=514.4 minutes. A second SRS of size 100100 has mean 𝑥¯=539.3x¯=539.3 minutes. After many SRSs, the values of the sample mean 𝑥¯x¯ follow the Normal distribution with mean 529.9529.9 minutes and standard deviation 13.5613.56 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¯x¯ describe? What is the sampling distribution?

a)The population is the 10,90010,900 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 529.9529.9 minutes and standard deviation 135.6135.6 minutes. B)The sampling distribution describes the distribution of the average sleep time for 100100 randomly selected individuals from this population. This distribution is Normal with mean 529.9529.9 minutes and standard deviation 13.5613.56 minutes.

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 𝑋X is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample, then 𝑋X has approximately:

an N(20,4) distribution.

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%70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 1010 word errors. (a) If the student matches the usual 70%70% rate, what is the distribution of the number of errors caught? -If the student matches the usual 70%70% rate, what is the distribution of the number of errors missed?

binomial, with 𝑛=10 and 𝑝=0.7 binomial, with 𝑛=10 and 𝑝=0.3

To obtain a smaller margin of error:

choose a larger sample size.

To obtain a smaller margin of error:

choose a smaller confidence level

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

false

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

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 200200 young American men with 100100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter (𝑘𝑔/𝑚2)(kg/m2) of fat‑free body mass. Typical young men have about 2020 𝑘𝑔/𝑚2kg/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 𝑘𝑔/𝑚22.35 kg/m2 . Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5 𝑘𝑔/𝑚22.5 kg/m2 . Give a 90%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 𝑘𝑔/𝑚^2 upper limit=2.6408 𝑘𝑔/𝑚^2

According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic black males was 71.8 years.71.8 years. Assume that the standard deviation was 15 years,15 years, as suggested by the Bureau of Economic Research. The distribution of age at death, 𝑋,X, is not normal because it is skewed to the left. Nevertheless, the distribution of the mean, 𝑥⎯⎯⎯,x¯, in all possible samples of size 𝑛n is approximately normal if 𝑛n is large enough, by the central limit theorem. Let 𝑥⎯⎯⎯x¯ be the mean life expectancy in a sample of 100100 non‑Hispanic black males. Determine the interval centered at the population mean 𝜇μ such that 95%95% of sample means 𝑥⎯⎯⎯x¯ will fall in the interval. Give your answers precise to one decimal. You may need to use software or a table of 𝑧-z-critical values.

lower limit= 68.9 years upper limit= 74.7 years

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

no

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 8686 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8080 mg/mi and standard deviation 44 mg/mi. (a) What is the probability that a single car of this model emits more than 8686 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 2525 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level 𝑥¯x¯ of these cars is above 8686 mg/mi? (Enter your answer rounded to four decimal places.)

probability: 0.0668 probability: 0

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 8686 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8282 mg/mi and standard deviation 55 mg/mi. (a) What is the probability that a single car of this model emits more than 8686 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 2525 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level 𝑥¯x¯ of these cars is above 8686 mg/mi? (Enter your answer rounded to four decimal places.)

probability: 0.2119 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 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500500 . In answering the questions, use 𝑧z‑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 495495 and 505505 ? Use Table A, or software to calculate your answer. (Enter your answer rounded to four decimal places.) (b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score 𝑥¯x¯ ? (Enter your answer rounded to two decimal places.)

probability: 0.3566 standard deviation: 1.8

A box at a miniature golf course contains contains 88 red golf balls, 77 green golf balls, and 66 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: 66.67%

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 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495495 . In answering the questions, use 𝑧z‑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 490490 and 500500 ? Use Table A, or software to calculate your answer. (Enter your answer rounded to four decimal places.) (b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score 𝑥¯x¯ ? (Enter your answer rounded to two decimal places.) c) What is the probability that the mean score of your sample is between 490490 and 500500 ? (Enter your answer rounded to four decimal places.)

probability:0.3544 standard deviation:1.8 probability:0.9944

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 6.36.3 . You want your sample mean 𝑥¯x¯ to estimate 𝜇μ with an error of no more than 1.31.3 point in either direction. (a) What standard deviation must 𝑥¯x¯ have so that 99.7%99.7% of all samples give an 𝑥¯x¯ within 1.31.3 point of 𝜇μ ? Use the 68-95-99.768-95-99.7 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¯x¯ to the value you found? (Enter your answer rounded to the nearest whole number.)

standard deviation of 𝑥¯=0.433 SRS size =212

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) =n!/k!(n−k!) , gives what information?

the number of ways in which 𝑘k successes in 𝑛n 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.

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

the sample mean approaches the population mean.

Suppose a clinical trial for a weight loss drug measured weight loss over a 4‑week period, both in patients taking the newly proposed drug and in those taking a placebo. The average weight loss was 10 pounds for the group getting the drug, and the placebo group lost an average of 2 pounds over the 4‑week period. We can say that:

users may or may not lose more on the newly proposed drug

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 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 9090 mg/mi and standard deviation 44 mg/mi. A company has 2525 cars of this model in its fleet. Using Table A, find the level 𝐿L such that the probability that the average NOX + NMOG level 𝑥¯x¯ for the fleet greater than 𝐿L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

𝐿=91.504

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,𝜎)

𝑁(𝜇,/𝜎√𝑛)

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,𝜎/√n)

In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 53% majored in business or commerce; 17% majored in engineering; 17% majored in the social sciences; 7% majored in the sciences; 4% majored in the humanities; and 2% listed some major other than the preceding. Assume there are no double majors. (a) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.) Select the probability rule you used to find the answer. (b) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.) Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce.

𝑃= 24% Rule 3.3. Two events 𝐴A and 𝐵B are disjoint if they have no outcomes in common and so can never occur together. If 𝐴A and 𝐵B are disjoint, 𝑃(𝐴 or 𝐵)=𝑃(𝐴)+𝑃(𝐵). p= 47% Rule 4.4. For any event 𝐴,A, 𝑃(𝐴 does not occur)=1−𝑃(𝐴).

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 𝑆S 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}

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

𝑛=30 , 𝑝=0.8