Statistics Fundamentals Unit 3 Milestone, Exams of Statistics

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Statistics Fundamentals Unit 3 Milestone You passed this Milestone 21 questions were answered correctly. 6 questions were answered incorrectly. 1 What is the probability of drawing a spade or a jack from a standard deck of 52 cards?

RATIONALE

Since it is possible for a card to be a spade and a jack, these two events are overlapping. We can use the following formula:

In a standard deck of cards, there are 13 cards that have Spade as their suit, so.

There is a total of 4 Jacks, so. Of the 4 Jacks, only one is spade so.

CONCEPT

A survey asked 1,000 people which magazine they preferred, given three choices. The table below breaks the votes down by magazine and age group.

Age Below 40 Age 40 and Above The National Journal 104 200 Newsday 120 230 The Month 240 106

If a survey is selected at random, what is the probability that the person voted for "Newsday" and is also age 40 or older? Answer choices are rounded to the hundredths place.

RATIONALE

If we want the probability of people who voted for "Newsday" and are also age 40 and over, we just need to look at the box that is associated with both categories, or 230. To calculate the probability, we can use the following formula:

CONCEPT

Mark noticed that the probability that a certain player hits a home run in a single game is 0.175. Mark is interested in the variability of the number of home runs if this player plays 200 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games? Answer choices are rounded to the hundredths place.

RATIONALE

Recall that we can go from " " odds to a probability by rewriting it as the fraction "

". So odds of 1:3 is equivalent to the following probability:

CONCEPT

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

RATIONALE

To find the probability that event A or event B occurs, we can use the following formula for overlapping events:

The probability of event A is ALL of circle A, or 0.43 + 0.11 = 0.54. The probability of event B is ALL of circle B, or 0.23 + 0.11 = 0.34. The probability of event A and B is the intersection of the Venn diagram, or 0.11.

We can also simply add up all the parts = 0.43 + 0.11 + 0.23 = 0.77.

CONCEPT

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

RATIONALE

Since we are looking for the probability until the first success, we will use the following Geometric distribution formula:

The variable k is the number of trials until the first success, which in this case, is 5 attempts. The variable p is the probability of success, which in this case, a success is considered missing a free throw. If the basketball player has an 80% of making it, he has a 20%, or 0.20, chance of missing.

CONCEPT

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

RATIONALE

To get the probability of B given A has occurred, we can use the following conditional formula:

The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.41. The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65.

CONCEPT

A credit card company surveys 125 of its customers to ask about satisfaction with customer service. The results of the survey, divided by gender, are shown below.

Males Females Extremely Satisfied 25 7 Satisfied 21 13 Neutral 13 16 Dissatisfied 9 14 Extremely Dissatisfied 2 5

If you were to choose a female from the group, what is the probability that she is satisfied with the company's customer service? Answer choices are rounded to the hundredths place.

The expected value is equal to the number of successes in the experiment.

• The sum of the probabilities of successes and failures is always 1.
• All trials are dependent.
• There are exactly three possible outcomes for each trial.

A probability distribution showing the number of pages employees read during the workday.

A probability distribution showing the number of minutes employees spend at lunch.

RATIONALE

For a distribution to be continuous, there must be an infinite number of possibilities. Since we are measuring the time to drive to work, there are an infinite number of values we might observe, for example: 2 hours, 30 minutes, 40 seconds, etc.

CONCEPT

Which of the following is a property of binomial distributions?

RATIONALE

Recall that for any probability distribution, the sum of all the probabilities must sum to

CONCEPT

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?

If Tracie spins the spinner 1,000 times, the relative frequency of it landing on red will remain constant.

The theoretical probability of the spinner landing on red will change with every spin completed.

If Tracie spins the spinner 4 times, it will land on red at least once.

If Tracie spins the spinner 1,000 times, it would land on red close to 250 times.

RATIONALE

If we make the assumption that the area of the colors represents the true proportion, then each color is equally weighted. Since there are four colors we would expect them to come up roughly 1/4 of the time. So on 1000 rolls the expected value = np = 10000.25 = 250.

CONCEPT

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

Sending a guilty man to jail.

• A medical test coming back negative for a disease you don't have.
• Sending an innocent man to jail.
• A medical test coming back positive for a disease you do have.

Red, red

Blue, black

RATIONALE

Since black is not part of the original set, it cannot be chosen into the sample.

CONCEPT

Which of the following is an example of a false positive?

RATIONALE

Sending a man to jail, when in fact he is innocent, is a false positive.

CONCEPT

Two sets A and B are shown in the Venn diagram below.

Set A has 12 elements.

• Sets A and B have 15 common elements.
• There are a total of 17 elements shown in the Venn diagram.
• Set B has 5 elements.

Which statement is TRUE?

RATIONALE

The number of elements of Set A is everything in Circle A, or 10+2 = 12 elements.

The number of elements of Set B is everything in Circle B, or 5+2 = 7 elements, not 5 elements. The intersection, or middle section, would show the common elements, which is 2 elements, not 15 elements. To get the total number of items in the Venn diagram, we add up what is in A and B and outside, which is 10+2+5+3 = 20 elements, not 17 elements.

CONCEPT

Patricia was having fun playing poker. She needed the next two cards dealt to be spades so she could make a flush (five cards of the same suit). There are 12 cards left in the deck, and three are spades. What is the probability that the two cards dealt to Patricia (without replacement) will both be spades? Answer choices are in percentage format, rounded to the nearest whole number.

RATIONALE

The expected value, also called the mean of a probability distribution, is found by adding the products of each individual outcome and its probability. We can use the following formula to calculate the expected value, E(X):

CONCEPT

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?

RATIONALE

We can use the general counting principle and note that for each step, we simply multiply all the possibilities at each step to get the total number of outcomes. Each die has 6 possible outcomes. So the overall number of outcomes for rolling 3 die with 6 possible outcomes each is:

CONCEPT

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?

False Positive

• False Negative
• Benford's Law

RATIONALE

The probability that Ryan will pick a red marble on the first try would be 20/60, or 33%. If Ryan keeps the red marble and doesn't replace it, then the likelihood of a green marble goes from 40/60, or 0.66, from the first try, to 40/59, or 0.678, on the second try. The second try has a higher probability.

CONCEPT

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. Which paradox has Kate encountered?

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 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 67%. 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 decreases.

The average number of tunnel construction projects that take place at any one time in a certain state is 3.

Find the probability of exactly five tunnel construction projects taking place in this state.

RATIONALE

Since we are finding the probability of a given number of events happening in a fixed interval when the events occur independently and the average rate of occurrence is known, we can use the following Poisson distribution formula:

The variable k is the given number of occurrences, which in this case, is 5 projects. The variable λ is the average rate of event occurrences, which in this case, is 3 projects.

CONCEPT

Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace. Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number.

RATIONALE

Since the two events, drawing a face card and drawing an ace card, are non- overlapping, we can use the following formula:

CONCEPT

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

RATIONALE

Recall that the probability of a complement, or the probability of something NOT happening, can be calculated by finding the probability of that event happening, and