katakana

z-score

(value-mean)/standard deviation

The number of ways a five-member committee can be chosen from 12 people.

Combination. The order of the committee members does not matter.

Distance a baseball travels after being hit.

Continuous, because distance is a random variable that is uncountable.

The temperature of a person taken with a mercury thermometer.

Continuous, because the temp. is random variable that cannot be counted.

in a binomial experiment, what does it mean to say that each trial is independent of the other trials?

Each trial is independent of the other trials of the outcome if one trial does not affect the outcome of any of the other trials.

You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a red four.

Event C has 2 outcomes. Event C is NOT a simple event because it has MORE THAN one outcome.

A combination is an ordered arrangement of objects.

FALSE. A permutation is an ordered arrangement of objects.

It is impossible to have a z-score of 0.

FALSE. A z-score of 0 is a standardized value that is equal to the mean.

An outlier is any number above Q3 or below Q4

FALSE. An outlier is any number above Q3 + 1.5(IQR) or below Q1 - (IQR).

The 50th percentile is equivalent to Q1

FALSE. The 50th percentile is equivalent to Q2.

A placebo is an actual treatment.

False. A placebo is a fake treatment.

A sample statistic will not change from sample to sample.

False. A sample statistic can change from sample to sample.

A statistic is a measure that describes a population characteristic.

False. A statistic is a measure that describes a sample characteristic.

The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals

False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.

Find the indicated area under the standard normal curve. To the LEFT of z = -2.58

Find -2.58 on chart.

Find the indicated area under the standard normal curve. BETWEEN: z = 0, z = 2.89

Find 0 and 2.89 on chart. Subtract 1 from those chart numbers. Then subtract the smaller number from the larger number.

Find the indicated area under the standard normal curve. To the RIGHT of z = 0.87

Find 0.87 on chart and subtract it from 1.

Find the area between z = -1 and z = 1.4 under the standard normal curve.

Find corresponding z-scores on chart. Subtract smaller z-score from larger z-score.

Use the given minimum and maximum data entries, and the number of classes to find the class width, the lower class limits, and the upper class limits.

Find the range: Subtract minimum from maximum Find the class width: Range divided by number of classes Lower class limit: Minimum + Class width (repeat this for number of classes) Upper limit: One less than the lower limit of the second class and add class width for as many classes given.

Find area of shaded region with a mean = 0, and standard deviation = 1

Find z-score on chart.

Find the area of the shaded region under the standard normal curve.

Find z-score on chart. Subtract that number from 1.

What is a disadvantage of using a stem-and-leaf plot instead of a histogram?

Histograms easily organize data of all sizes where stem-and-leaf plots do not.

After constructing a relative frequency distribution summarizing IQ score of college students, what should be the sum of the relative frequencies?

If percentages are used, the sum should be 100%. If proportions are used, the sum should be 1.

Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Every twelfth person entering a sporting goods store is asked to choose his or her favorite sport from a list of five different sports that includes a description of each.

If there is a regular pattern to the people entering the sporting goods store, the sample may not be representative. The wording of the question may direct respondents towards a particular sport.

What is the difference between an observational study and an experiment?

In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change the existing conditions.

What is the significance of the mean of a probability distribution?

It is the expected value of a discrete random variable.

Why is a sample used more often than a​ population?

It is usually impossible to count the entire population.

Eighty-four percent of adults in a certain country believe that life on other planets is plausible. You randomly select five adults and ask them whether they believe that life on other planets is plausible. The random variable represents the number of adults who believe that life on other planets is plausible. Find the mean, variance, and standard deviation of the binomial distribution for the random variable. Interpret the results.

Mean: 4.2 Variance: 1-.084*4.2*0.84 Standard deviation: Square root of variance.

What is the difference between a parameter and a​ statistic?

A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic.

How is a sample related to a population?

A sample is a subset of a population.

A standard deck of cards contains 52 cards. One card is selected from the deck. A) Compute the probability of randomly selecting an ace or king. B) Compute the probability of randomly selecting an ace or king or seven. C) Compute the probability of randomly selecting an eight or spade.

A) 4 aces + 4 kings = 8/52 B) 4 aces + 4 kings + 4 sevens = 12/52 C) 4 eights + 13 spades = 4/13

Mean

Add up all numbers and then divide by how many numbers are present.

Median

Arrange numbers in order and the middle number is the median.

Mode

Arrange numbers in order and the number that appears most often is the the mode.

79% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.

Mean: 6*0.79 Variance: 1-0.79*6*0.79 Standard Deviation: Square root of variance.

Find the mean, variance, and standard deviation of the binomial distribution with the given values of (n) and (p). n = 80 p = 0.6

Mean: multiply 80*0.6 Variance: 1 - 0.6, 80*0.6*0.4 Standard Deviation: Square root of variance.

Use the frequency distribution shown below to construct an expanded frequency distribution.

Midpoint: Lower class limit + Upper class limit, divided by 2 Relative Frequency: Class frequency divided by total sample size. Cumulative Frequency: Sum of current frequency and all frequencies before it.

A horse race has 10 entries and one person owns 5 of those horses. Assuming that there are no ties, what is the probability that those five horses finish first, second, third, fourth, and fifth (regardless of order)?

Multiply 1st through 5th (1*2*3*4*5) Multiply 6th through 10th(6*7*8*9*10) Divide 1-5 by 6-10 = .0040

A doctor gives a patient a 90% chance of surviving bypass surgery after a hear attack. If the patient survives the surgery, then the patient has a 40% chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals.

Multiply the 90% by 40% to get the probability. Prob. = 0.36

In a normal distribution, which is greater, the mean or the median?

Neither, in a normal distribution, the mean and the median are equal.

The jersey numbers for players on a soccer team are listed. Identify the level of measurement of the data set. Explain your reasoning.

Nominal. The data are categorized using numbers, but no mathematical computations can be made.

Classical probability for an event (E)

Number of outcomes in event E/Total number of outcomes in a sample space.

unusual z-score

Number outside the range of (-2) - 2

Name each level of measurement for which data can be qualitative.

Ordinal Nominal

Classical (theoretical) probability

Outcome in sample space is equally likely to occur.

Three formulas that can be used to describe complementary events.

P(E) = 1 - P(E) P(E) + P(E') = 1 P(E') = 1 - P(E)

What is a discrete Probability Distribution?

PD lists each possible value a random variable can assume, together with its probability.

How many different 3-letter passwords can be formed from the letters A,B,C,D,E,F, and G if no repetition of letters is allowed.

Permutation because the order in which the letters are selected does matter.

Determine whether the data set is a population or a sample. The number of floors in each home in a town

Population because it is a collection of the number of floors for all homes in the town.

A polling organization contacts 1558 adults who are 20 to 90 years of age and live in Europe and asks whether or not they had voted in the last federal election.

Population: Adults who are 20 to 90 years of age and live in Europe. Sample: the 1558 adults who are 20 to 90 years of age and live in Europe.

In a​ poll, 1004 adults in a country were asked whether they favor or oppose the use of​ "federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Among the​ respondents, 47​% said that they were in favor. Identify the population and the sample.

Population: All adults in the country. Sample: 1004 adults selected.

Empirical (statistical) probability

Probability is based on observations obtained from probability experiments.

IQR (interquartile range)

Q3-Q1

The heights (in inches) of a sample of species of tree two years after being planted are shown. Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.

Quantitative Ratio

The masses (in grams) of a sample of species of fish caught in the waters of a region are shown below. 19.1, 20.8, 20.2, 20.2, 17.3, 17.1, 16.2, 21.2, 19.3, Determine the level of measurement of the data set. Explain your reasoning.

Ratio. The data can be ordered and differences between data entries are meaningful, and a zero enter is an inherent zero.

Subjective probability

Results from intuition, educated guesses, and estimates.

Standard deviation of a data set.

Square root of the population variance, rounded to the nearest tenth.

Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.

The two curves will have THE SAME LINE of symmetry. The curve with the larger standard deviation will be MORE spread out than the curve with the smaller standard deviation.

Why is the standard deviation used more frequently than the variance?

The units of variance are squared. Its units are meaningless.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite brand of computer.

The variable is qualitative because a favorite brand describes an attribute or characteristic.

How to find Q1 and Q2

Use the median to divide data set into two halves. The median of the first half is Q1. The median of the second half is Q3.

What are the two main branches of​ statistics?

descriptive statistics and inferential statistics.

"THE" standard normal distribution.

mean: 0 standard deviation: 1

A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 10 choices for an entree, and 3 choices for a dessert. How many different meals are available when you select an app, entree, and a dessert?

multiply all choices to come up with 120 different meals.

Formula to convert an x value into a z-score

x - mean/standard deviation

A normal distribution

any mean and standard deviation

Determine which numbers could NOT be used to represent the probability of an event.

-1.5, because probability cannot be less than 0. 64/25, because probability values cannot be greater than 1.

What is the total area under the normal curve?

1

You randomly select a number from 0 to 49 (inclusively) and then randomly select a number from 0 to 4 (inclusively). What is the probability of selecting a 2 both times?

1/50 = 0.02 1/5 = 0.2 0.2*0.02 = 0.004

A physics class has 50 students. Of these, 15 students are physics majors and 13 are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major.

15/50 = 0.30 13/50 = 0.26 3/50 = 0.06 0.30 + 0.26 - 0.06 = 0.500

Empirical Rule

68%, 95%, 99.7%

26C2

Calc = 26, MATH, PRB, nCr, 2

42P2

Calc = 42, MATH, PRB, nPr, 2

What is the difference between class limits and class boundaries?

Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them.

The home attendance for a football game at a university.

Discrete, because home attendance is a random variable that is countable.

Deviation of a data set

Data entry minus the mean, then square that result.

A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the​ experiment: Amanda,​ Brian, Christine,​ David, Emily,​ Fred, George,​ Heather, and Ivan. Use the second row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). The other six subjects will go into the control group. If the subjects are numbered 1 - 9 alphabetically, what are the numbers of the three subjects selected? List the subjects that will go in the treatment group

Start at the first set of numbers in row 2 and pick the first three numbers that fall within 1 and 9 and that do not repeat. list them alphabetically.

Determine whether the **underlined** value is a parameter or a statistic. In a national survey of high school students (grades 9 to 12), **25%** of respondents reported that someone had offered, sold, or given them an illegal drug on school property. Is the value a parameter or a statistic?

Statistic

What is an advantage of using a stem-and-leaf plot instead of a histogram?

Stem-and_leaf plots contain original data values where histograms do not.

Mean of data set

Sum of all data entries divided by number of data entries.

Class boundaries ensure that consecutive bars of a histogram touch.

TRUE

If two events are mutually exclusive, they have no outcomes in common.

TRUE

The mean is the measure of central tendency most likely to be affected by an outlier.

TRUE

The midpoint of a class is the sum of its lower and upper limits divided by two.

TRUE

When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.

TRUE

Explain how the complement can be used to find the probability of getting at least one item of a particular type.

The compliment of "at least one" is "none". So the probability of getting at least one item is equal to 1 - P(non of the items)

If a z-score is 0.

The corresponding x-value is equal to the mean, because the z-score is equal to the difference between the x-value and the mean, divided by the standard deviation.

Range of data set

The difference between the lowest data value and highest data value.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and the standard deviation have the values of MEAN: 0 SD: 1

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 2216 adults in a country found that 75% think that militant terrorists are a major threat to the well-being of their country.

The number is a sample statistic because it describes the people in a sample, which is a subset of all the people in the country.

What are the two conditions that determine a probability distribution?

The probability of each value of the discrete random variable is between 0 and 1, inclusive, and the sum of all the probabilities is 1.

Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain.

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Determine whether the study is an observational study or an experiment. Explain. In a survey of 1469 adults in a country, 58% said the country's leader should release all medical information that might affect their ability to serve.

The study is OBSERVATIONAL, because it DOES NOT APPLY a treatment to the adults.

Population variance of a data set.

The sum of all squared deviations divided by number of data entries.

Calculation of population standard deviation

The sum of the squared deviation is divided by N, then the square root of the result is taken.

Sample standard deviation

The sum of the squared deviation is divided by n - 1, then the square root is taken.

EVENT A: Randomly select a male chemistry major. EVENT B: Randomly select a chemistry major who is 20 years old.

These events ARE NOT mutually exclusive, since IT IS POSSIBLE TO SELECT A MALE CHEMISTRY MAJOR WHO IS 20 YEARS OLD.

EVENT A: Randomly select a voter who is a registered member of the Reform Party. EVENT B: Randomly select a voter who is a registered Republican.

These events ARE mutually exclusive, since it IS NOT possible for a voter to both be a registered member of the Reform Party and BE a registered Republican.

Determine whether the data set is a population or a sample. The number of floors in 17 buildings in a city.

This is a sample because it is a collection of the number of floors for some buildings in the city.

About 90% of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

YES it is Binomial. Success = Baby recovers (n) = 7 (p) = 0.9 (q) = 0.1 (1-0.9) (x) = 0,1,2,...,7