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# Introduction to Statistics Unit 3 Milestone 3 Exam

Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games.

If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place.

4.55

20.67

0.91

24.75

Using the Venn Diagram below, what is the conditional probability of event Q occurring, assuming that event P has already happened [P (Q|P)]?

For a math assignment, Michelle rolls a set of three standard dice at the same time and notes the results of each trial.

What is the total number of outcomes for each trial?

18

36

216

27

A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble.

Which of the following statements is true?

The probability that Ryan will pick a red marble on the first try is 67%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.

The probability that Ryan will pick a red marble on the first try is 33%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.

The probability that Ryan will pick a red marble on the first try is 33%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

The probability that Ryan will pick a red marble on the first try is 67%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

What is the probability of drawing a spade or a jack from a standard deck of 52 cards?

Tim rolls two six-sided dice and flips a coin.

All of the following are possible outcomes, EXCEPT:

1, Tails, 6

5, 2, Tails

Which of the following is a condition of binomial probability distributions?

All observations made are dependent on each other.

All observations made are independent of each other.

All observations are mutually exclusive.

Annika was having fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit).  There are 15 cards left in the deck, and five are diamonds.

What is the probability that the two cards dealt to Annika (without replacement) will both be diamonds? Answer choices are in percentage format, rounded to the nearest whole number.

13%

10%

33%

29%

Using this Venn diagram, what is the probability that event A or event B occurs?

0.60

0.22

0.42

0.78

There is a 30% chance of rain tomorrow.

What are the odds in favor of it raining?

3:7

10:3

7:3

3:10

Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results.If you were to choose a boy from the group, what is the probability that mangoes are his favorite fruit?  Answer choices are rounded to the hundredths place.

Dida bought a scratch ticket for \$2.00.  The potential payoffs and probability of those payoffs are shown below. What is the expected value for the scratch ticket that Dida bought?

Which of the following situations describes a discrete distribution?

A probability distribution showing the heights of children in a first grade class.

A probability distribution showing the average time it takes for children to walk to school.

A probability distribution of the quantity of babies in the intensive care unit.

A probability distribution showing the weights of newborns.

A magician asks an audience member to pick any number from 6 to 15.

What is the theoretical probability that an individual chooses the number the magician has in mind?

Kate was trying to decide which type of frozen pizza to restock based on popularity: pepperoni pizza or sausage pizza. After studying the data, she noticed that pepperoni flavors sold best on the weekdays and on the weekends, but not best overall.

False Negative

False Positive

Benford’s Law

Maria flipped a coin 60 times, and the coin came up tails 32 times.

What is the relative frequency of the coin turning up heads in this experiment?  Answer choices are rounded to the hundredths place.

1.88

0.47

0.53

2.14

The average number of babies born at a private hospital’s maternity wing is 6 per hour.

What is the probability that three babies are born during a particular 1-hour period in this maternity wing?

0.09

0.16

0.13

0.20

Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a King of clubs or an Ace of clubs.

Choose the correct probability of drawing a King of clubs or an Ace of clubs. Answer choices are in the form of a percentage, rounded to the nearest whole number.

2%

8%

6%

4%

Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results.If a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit? Answer choices are rounded to the hundredths place.

What is the probability of NOT drawing a face card from a standard deck of 52 cards?

Tracie spins the four-colored spinner shown below.  She records the total number of times the spinner lands on the color red and constructs a graph to visualize her results.

Which of the following statements is TRUE?

Asmita went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards.

Asmita has had good luck at blackjack in the past, and she actually got three blackjacks with Aces in a row the last time she played. Because of this lucky run, Asmita thinks that Ace is the luckiest card.

The dealer deals the first card to her. In a split second, she can see that it is a non-face card, but she is unsure if it is an Ace.

What is the probability of the card being an Ace, given that it is a non-face card? Answer choices are in a percentage format, rounded to the nearest whole number.

Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card.

What is the probability of drawing a red card, placing it back in the deck, and drawing another red card?  Answer choices are in the form of a percentage, rounded to the nearest whole number.

13%

25%

4%

22%

A basketball player makes 60% of his free throws. We set him on the free throw line and asked him to shoot free throws until he misses. Let the random variable X be the number of free throws taken by the player until he misses.

Assuming that his shots are independent, find the probability that he will miss the shot on his 6th throw.

0.04666

0.01866

0.03110

0.00614

## Introduction to Statistics Unit 3 Milestone 3 Exam

Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games.

If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place.

4.55

20.67

0.91

24.75

Using the Venn Diagram below, what is the conditional probability of event Q occurring, assuming that event P has already happened [P (Q|P)]?

For a math assignment, Michelle rolls a set of three standard dice at the same time and notes the results of each trial.

What is the total number of outcomes for each trial?

18

36

216

27

A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble.

Which of the following statements is true?

The probability that Ryan will pick a red marble on the first try is 67%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.

The probability that Ryan will pick a red marble on the first try is 33%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.

The probability that Ryan will pick a red marble on the first try is 33%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

The probability that Ryan will pick a red marble on the first try is 67%.  If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

What is the probability of drawing a spade or a jack from a standard deck of 52 cards?

Tim rolls two six-sided dice and flips a coin.

All of the following are possible outcomes, EXCEPT:

1, Tails, 6

5, 2, Tails

Which of the following is a condition of binomial probability distributions?

All observations made are dependent on each other.

All observations made are independent of each other.

All observations are mutually exclusive.

Annika was having fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit).  There are 15 cards left in the deck, and five are diamonds.

What is the probability that the two cards dealt to Annika (without replacement) will both be diamonds? Answer choices are in percentage format, rounded to the nearest whole number.

13%

10%

33%

29%

Using this Venn diagram, what is the probability that event A or event B occurs?

0.60

0.22

0.42

0.78

There is a 30% chance of rain tomorrow.

What are the odds in favor of it raining?

3:7

10:3

7:3

3:10

Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results.If you were to choose a boy from the group, what is the probability that mangoes are his favorite fruit?  Answer choices are rounded to the hundredths place.

Dida bought a scratch ticket for \$2.00.  The potential payoffs and probability of those payoffs are shown below. What is the expected value for the scratch ticket that Dida bought?

Which of the following situations describes a discrete distribution?

A probability distribution showing the heights of children in a first grade class.

A probability distribution showing the average time it takes for children to walk to school.

A probability distribution of the quantity of babies in the intensive care unit.

A probability distribution showing the weights of newborns.

A magician asks an audience member to pick any number from 6 to 15.

What is the theoretical probability that an individual chooses the number the magician has in mind?

Kate was trying to decide which type of frozen pizza to restock based on popularity: pepperoni pizza or sausage pizza. After studying the data, she noticed that pepperoni flavors sold best on the weekdays and on the weekends, but not best overall.

False Negative

False Positive

Benford’s Law

Maria flipped a coin 60 times, and the coin came up tails 32 times.

What is the relative frequency of the coin turning up heads in this experiment?  Answer choices are rounded to the hundredths place.

1.88

0.47

0.53

2.14

The average number of babies born at a private hospital’s maternity wing is 6 per hour.

What is the probability that three babies are born during a particular 1-hour period in this maternity wing?

0.09

0.16

0.13

0.20

Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a King of clubs or an Ace of clubs.

Choose the correct probability of drawing a King of clubs or an Ace of clubs. Answer choices are in the form of a percentage, rounded to the nearest whole number.

2%

8%

6%

4%

Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results.If a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit? Answer choices are rounded to the hundredths place.

What is the probability of NOT drawing a face card from a standard deck of 52 cards?

Tracie spins the four-colored spinner shown below.  She records the total number of times the spinner lands on the color red and constructs a graph to visualize her results.

Which of the following statements is TRUE?

Asmita went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards.

Asmita has had good luck at blackjack in the past, and she actually got three blackjacks with Aces in a row the last time she played. Because of this lucky run, Asmita thinks that Ace is the luckiest card.

The dealer deals the first card to her. In a split second, she can see that it is a non-face card, but she is unsure if it is an Ace.

What is the probability of the card being an Ace, given that it is a non-face card? Answer choices are in a percentage format, rounded to the nearest whole number.

Eric is randomly drawing cards from a deck of 52. He first draws a red card, places it back in the deck, shuffles the deck, and then draws another card.

What is the probability of drawing a red card, placing it back in the deck, and drawing another red card?  Answer choices are in the form of a percentage, rounded to the nearest whole number.

13%

25%

4%

22%

A basketball player makes 60% of his free throws. We set him on the free throw line and asked him to shoot free throws until he misses. Let the random variable X be the number of free throws taken by the player until he misses.

Assuming that his shots are independent, find the probability that he will miss the shot on his 6th throw.

0.04666

0.01866

0.03110

0.00614

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