Statistics 101

In a poker game with a standard 52 card deck, what is the probability of getting a five-card hand with 4 jacks and a king?

1 in 649,740

A bag has 5 blue pens, 2 red pens, 2 green pens and 1 yellow pen. What is the probability of drawing 2 successive red pens?

1/45

A company has revenue as described in the table. Using the data from the table, what is the interquartile range of the company's revenue?

15,000

Three coins are tossed. What is the possibility of two of them being heads?

3/8

Find the variance for the following data set: (rounding the answer to the nearest tenth). 16, 20, 14, 24, 16, 19, 30, and 8

38.5

On a history exam, the average score was 75, with a standard deviation of 15. Assume that the distribution of the scores is normal. What percentage of the class scored between 60 and 80 points?

47%

A researcher has conducted an analysis and believes that for every hour a student sleeps in beyond an 8 hour nightly sleep period, he will achieve 10 more points on a test that goes up to 100 points. Assume that the student starts with a failing grade of 50. What is the likely y-intercept of the researcher's regression equation?

50

The stem and leaf plot shown below shows the number of aces hit by the world's best tennis players in the past month. What percentage of players hit more than 29 aces?

67%

James is going through an old bag of marbles. He bets his friends that he can pull a red marble out of the bag and then a yellow marble in one try. There are 12 red marbles and 7 yellow marbles. What is the probability that he can pull a yellow from the bag, given that he has already pulled a red?

7/18

A package of sweet food has 10 cookies, 10 cakes, 10 waffles and 10 small pieces of candy. You have randomly taken food from the package and retrieved a cookie. Without returning the cookie you have again tried to take something from the package. What is the probability you will once again retrieve a cookie?

9/39

What is game theory?

A field of math used to guide logical decision making

How do you find the mean of a data set?

Add up all the values in the data set, then divide by the total number of values in the data set.

Which of the following statements is TRUE in regards to a binomial experiment?

All choices are true.

What is the expected value of 79 customers purchasing a spoon tie if the success probability is 35

Approximately 28 customers

Binomial formula

B(x;n,p) = nCx * P * (1-P)^n-x

Which of the following assigns probabilities to the potential values of the variable x?

Binomial formula

_____ data can be divided infinitely, while _____ data can only occur in certain values.

Continuous, discrete

Which of the following best defines a residual?

The difference between an observed value and its corresponding predicted value

Which of the following is an implication of the central limit theorem?

The mean of the population can be approximated by the mean of the sample means.

What does the central limit theorem state?

The more you run a random experiment, the more its results will follow a normal distribution.

Correlation

The relationship between two sets of variables used to describe or predict information

A researcher is studying a population, and decides to use simple random sampling. Why might they have made this decision?

The researcher doesn't know a lot about the population.

A scatter plot displays the relationship between how much people study (x) and the time they spend playing sports (y). What is the relationship between the variables?

There is no relationship or a weak relationship

Which of the following is TRUE about continuous random variables?

They involve processes where the total number of possible outcomes is uncountable.

A scientist is measuring the diameters of tree trunks, measuring twenty trees per trip. If the scientist increases their sample size to thirty per trip, then what change should they expect to see in the means of the samples?

They will become more normally distributed.

The monthly revenue of several companies with their names abbreviated is presented in the table. If a company is in the 75th percentile, in which quartile is it?

Third

Solving for the expected value of a continuous probability distribution involves _____.

integration

A bag of candy which has 100 pieces of candy has 15 yellow pieces, 17 green pieces, 18 red pieces, 20 blue pieces and 30 orange pieces. What is the probability that you will draw an orange or blue piece?

1/2

A study has shown that there is a 40% chance that people who are 25 will still be alive when they are 85 years old. The researcher had randomly selected 3 college students aged 25. By using the binomial probability formula, what is the probability that the number alive at age 85 is at least 1?

43.2%

In a game of blackjack where you are the only player, the first card you draw is the king and the second is an eight. You decide to draw another card. What is the probability that upon drawing another card, you will lose (go over 21)? Assume that aces can count as 1 and you are playing with a standard 52 card deck.

76%

The law of large numbers is also known as:

Bernoulli's law.

What is the number of successes in a binomial experiment called?

Binomial Random Variable

What is the name for the line that goes through the mean of a normal distribution curve?

Central line

_____ is a sampling method where different groups within a population are used as a sample.

Cluster sampling

Identify which of the following is an example of a histogram:

Picture

What is a set (S) of a random experiment that includes all possible outcomes of the experiment?

Sample space

To use systematic random sampling, you must first create a list of your population, and then:

Select a beginning number

Which type of random sampling divides members of a population into homogeneous subgroups?

Stratified random sampling

regression analysis

Study of two variables in an attempt to find a relationship or, correlation

What is the method that requires selecting samples based on a system of intervals in a numbered population?

Systematic random sampling

In regression analysis, what would a linear correlation coefficient with a value r=0.01 suggest?

That there is very little or no connection between the variables

Permutation

nPr=n!/(n-r)!

You should use cluster sampling when the clusters are _____ in a population.

natural

In a school math competition, the order of winners is an example of _____ data.

ordinal

A tobacco company is trying to increase its appeal to young working class people. They have randomly taken 100 participants from that age group and are asking how they should market their products. The number of young working class people is _____.

quantitative and discrete

For the data shown bellow, calculate the linear correlation coefficient:

r=-0.6686

To find the interval you need, take your population divide by the _____.

sample size

Standard deviation

sqrt(n*P*(1-P))

The _____ is a measure of distance from the mean in terms of how many standard deviations it is removed from the mean.

z-score

Z-score formula

z=(x-mean)/standard deviation

A news station has planned to invest $50,000 this year in advertising and plans to decrease the amount they spend in advertising by $5,000 each year for the next 10 years. If x represents the number of years passed and y the value of their investment in advertising, how much will they spend on advertising at two years? (Using this information, write a linear equation and substitute in the number of years to find the answer.)

$40,000

Suppose you play a game where you roll 2 six-sided dice. If you roll a 7, you will lose some money, but if you roll anything else you will win $1. How much money would you have to lose in order for you average $0 per roll?

$5

Your manager is asking you to measure the relationship between the amount of money spent on advertisement (x) and the number of products consumers buy (y). Based on the following data and by calculating the regression equation, how much money do you need to spend to sell 20 products?

$82

The probability of selecting a red M&M from a bag is 2/5. If 5 M&Ms are selected, what is the probability of at least one M&M being red?

0.922

Thomson Industries needs to maintain its average quarterly revenue to be at least $150,000 or else the interest rates on their loans will go up. If their revenue is as displayed in the following table, what is the LEAST that they have to make in the fourth quarter in order to avoid the higher interest rates?

216,000

A researcher is conducting studies about the average weight and height of college students. Their height is in centimeters and their weight is in pounds. Their names were substituted with numbers in order to conceal their identities. What is the standard deviation of their weight?

26.96

A study has shown that there is a 40% chance that people who are 25 will still be alive when they are 85 years old. The researcher had randomly selected 3 college students aged 25. By using the binomial probability formula, what is the probability that the number alive at age 85 will be exactly two?

28.8%

Mark conducted a math test and the mean result of his students was 73, with a variance of 49 (standard deviation = 7). The grade excellent was achieved by all students who scored 86 points or higher. Assume that the grades are normally distributed and the class has 100 students. How many students managed to get an excellent grade?

3

Elizabeth wanted to know the gender and the hair color of each of her classmates. She arranged the results of this survey into a two-way table, shown below. According to the table, what is the joint relative frequency of boys with red hair?

3/27

Russell is a history teacher who recently held an exam in his class. The mean score result is 65, while the standard deviation was 20. Assume that the scores are normally distributed. If a student's z-score was 1.5, how many points did he score on the exam?

95

Tom is playing a game of craps and and if the sum is 7 or 11, then he wins. If the sum is 2, 3 or 12, then he loses. If the sum is anything else, then he/she continues throwing until that number appears again, or he throws a 7, where the game ends in a loss. What would a binomial distribution of the data allow us to do?

Calculate the probability of what each toss will do.

What is data that is collected in groups or topics, where the number of events in each group is counted numerically?

Categorical data

You are pulling cards from a standard 52-card deck. For which of the following is the probability 12 / 2652? (You do not replace the card pulled.)You are pulling cards from a standard 52-card deck. For which of the following is the probability 12 / 2652? (You do not replace the card pulled.)

Drawing two consecutive kings

According to the law of large numbers, the difference between the theoretical probability and the experimental probability becomes _____ as more experiments are performed, or as the sample size gets larger.

smaller

A newspaper agency has a new employee with a starting salary of $1600, but they plan to increase it by $140 each year for the next 5 years. If x represents how long he works there in years, and y represents his salary in dollars, what is the linear equation?

y = 140x + 1600

A CEO is measuring how an increase in the pay of his employees (x) impacts how long they voluntarily stay at work (y). What is the regression equation for this data?

y = 3x + 1

What does the following scatter plot suggest (r=.98)?

That there is a strong positive correlation

Three coins are tossed. For which of the following is the probability 7/8?

That there will be at least one tails

Bar charts are best used to represent _____ data.

categorical

Data on the result of an exam in high school was collected. Which of the following BEST describes this form of visual representation of data?

Histogram

Which of the following r values would suggest that the regression equation is very useful for making predictions, either positive or negative?

If r is close to or equal -1 or 1

Identify in which of the following cases is the probability 11/221:

If, in a game of blackjack, you were to draw 2 face cards (king, queen, or jack) in a row.

Which of the following is a way of increasing the power of a hypothesis test?

Increasing the sample size.

What are groups of information that are scaled and separated equally?

Intervals

Which of the following is FALSE regarding the binomial probability distribution?

It is calculated based on a formula where p is the significance level for a single event and q is the quantity of data present.

Which of the following conditions must be met for a sample to be a stratified random sample?

It must include all members of a population.

You're drawing a card from a standard deck with 52 cards. For which of the following is your probability of drawing this card 2:13?

It's the probability of drawing a jack or a ten.

Which is a sampling method that involves separating the population into clusters, and then selecting random samples from each of the clusters?

Two-way cluster sampling.

Which of the following is a way of increasing the power of a hypothesis test?

Using a stratified sampling technique.

Which of the following is NOT an example of descriptive data?

Using samples to predict how the entire population will respond

Identify which of the following distributions has the largest spread:

When the mean is 11 and the standard deviation is 4.

Dr. Matthews wants to know how many veterinary students decide to pursue a career as small animal practitioners. There are 27 veterinary schools in the USA, so he decides to randomly select 10% of the students from each school and asks them where they intend to practice once they finish veterinary school. Is this an example of a simple random sample?

Yes, because each student of the 27 colleges had an equal chance of being sampled.

Suppose you play a game where you roll a set of 2 fair dice. If you roll a 4, 5, or 6, you will lose $6, but if you roll anything else, then you win $3. How much money will you gain or lose per each throwing?

You will average exactly 0 per each throwing of the dice.

You have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get at least 14 heads. What is the probability that you will get heads MORE than 14 times?

2%

If z = 2 and -2, what area falls OUTSIDE these z values on a standard normal curve?

0.046

Gary has a deck of 52 cards. He wants to know the probability of drawing the jack of spades and then drawing the two of hearts from the deck without replacing either card. What's the probability of this event? (A standard deck of 52 cards has 4 suits (hearts, clubs, spades, diamonds), each with 13 cards. Each suit has an ace, cards numbered 2 through 10, and a jack, a queen, and a king.)

1/2652

Tom is playing a game of craps and if the sum is 7 or 11, then he wins. If the sum is 2, 3 or 12, then he loses. If the sum is anything else, then he continues throwing until that number appears again, or he throws a 7, where the game ends in a loss. If the probability is 0.4929, what is the probability of him winning in the first throw by getting a 7?

1/6

On a 20-sided die, each side shows a number from 1-20. What is the probability that the sum of the numbers shown will be 6 when rolling two?

1/80

Mrs. Allison is preparing a cookies and milk party for her third grade class. There are 12 students that drink only whole milk, 8 students that drink only almond milk, 7 students that drink only skim milk, and 3 students that drink only soy milk. What is the probability that a student from Mrs. Allison's class drinks only almond or soy milk?

11/30

The Davis Cup tennis coach has 4 players and is trying to decide which two he is going to send to play the crucial doubles match. The coach is going to announce the top 2 players in order and they will play the match. In how many different ways could the coach choose and order his players?

12

What is the standard deviation for the following dataset? {12, 4, 52, 4, 31, 3, 6, 13}

16.2

What is the mode of the following data set? {1, 2, 6, 8, 6, 2, 16, 14, 11, 2}

2

Why would using a median be more representative than a mode for the revenue of this company?

Because most of the values are similar, with only two values that won't skew the median

If a data set has a large standard error, then what does that imply about the data set?

That the data set represents a broad range of numbers

Suppose you play a game where you roll 2 six-sided dice. If you roll a 7, you gain $108, but if you roll anything else, you lose $12. How much money will you gain or lose per each throwing?

You will, on average, earn $8 per each throwing of the dice.

What is a probability formula that uses factorials to find the number of possible combinations of all the outcomes in the experiment?

combination formula