chance behavior is UNPREDICTABLE in the short run, but has a PREDICTABLE PATTERN in the long run.

…

If individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions we call the phenomenon:

RANDOM

Probability can be written as a:

Fraction, Decimal, Percent

The range of values of probability is:

0-1

Probability is a measure of how likely an event is to occur. Which probability best matches the following event:

The probability that tomorrow is Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

The probability that tomorrow is Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

1.0

Probability is a measure of how likely an event is to occur. Which probability best matches the following event: The probability that the toss of fair coin will land on tails.

0.5

Probability is a measure of how likely an event is to occur. Which probability best matches the following event: The probability that it will snow when it’s 100 degrees outside.

Probability is a measure of how likely an event is to occur. Which probability best matches the following event: The probability that you will get into a car accident while driving.

0.2

Gambling often uses:

ODDS

Joe goes to the roulette table and sees that the last five numbers called were red. He immediately puts all his money on black stating that black HAS to be the next number called. What myth is Joe employing?

Myth of the law of averages

A PROBABILITY MODEL describes how we assign probabilities to a collection of outcomes.

…

Which is not a probability rule?

Any probability is a number between 0 and 100.

The probability that it will rain tomorrow is 0.4. What is P(no rain)?

0.6

If you draw a chocolate truffle from a bag of chocolates, the one you draw will have one of five flavors. The probability of drawing each truffle depends on the proportion of each flavor among all flavors made. Here are the probabilities of each flavor for a randomly chosen bag of chocolates:

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(White Chocolate)?

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(White Chocolate)?

0.1

If you draw a chocolate truffle from a bag of chocolates, the one you draw will have one of five flavors. The probability of drawing each truffle depends on the proportion of each flavor among all flavors made. Here are the probabilities of each flavor for a randomly chosen bag of chocolates:

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(not Raspberry)?

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(not Raspberry)?

0.75

If you draw a chocolate truffle from a bag of chocolates, the one you draw will have one of five flavors. The probability of drawing each truffle depends on the proportion of each flavor among all flavors made. Here are the probabilities of each flavor for a randomly chosen bag of chocolates:

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(Dark Chocolate or Peanut Butter)?

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(Dark Chocolate or Peanut Butter)?

0.45

If you draw a chocolate truffle from a bag of chocolates, the one you draw will have one of five flavors. The probability of drawing each truffle depends on the proportion of each flavor among all flavors made. Here are the probabilities of each flavor for a randomly chosen bag of chocolates:

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(Orange)?

raspberry .25

dark chocolate 0.3

mint 0.2

peanut butter 0.15

white chocolate ?

What is the P(Orange)?

An opinion poll asks an SRS of 1000 adults “Do you watch American Idol?” Suppose (as is approximately correct) the proportion of the population that watches American Idol is p = 0.35. In a large number of samples, the proportion who answer that they watch American Idol will be approximately Normally distributed with a mean of 0.35 and a standard deviation of 0.10. Answer the following question using the 68-95-99.7 Rule.

What percentage of the samples will have a sample proportion who watch American Idol of 0.35 or higher?

What percentage of the samples will have a sample proportion who watch American Idol of 0.35 or higher?

50%

An opinion poll asks an SRS of 1000 adults “Do you watch American Idol?” Suppose (as is approximately correct) the proportion of the population that watches American Idol is p = 0.35. In a large number of samples, the proportion who answer that they watch American Idol will be approximately Normally distributed with a mean of 0.35 and a standard deviation of 0.10. Answer the following question using the 68-95-99.7 Rule.

What is the probability that > will take a value between 0.25 and 0.45?

What is the probability that > will take a value between 0.25 and 0.45?

68%

An opinion poll asks an SRS of 1000 adults “Do you watch American Idol?” Suppose (as is approximately correct) the proportion of the population that watches American Idol is p = 0.35. In a large number of samples, the proportion who answer that they watch American Idol will be approximately Normally distributed with a mean of 0.35 and a standard deviation of 0.10. Answer the following question using the 68-95-99.7 Rule.

What is the probability that does not lie between 0.25 and 0.45?

What is the probability that does not lie between 0.25 and 0.45?

0.32

The expected value of a random phenomenon is:

The weighted average of all possible outcomes; The sum of the products of numerical outcomes and their respective probabilities

The expected value of a six-sided fair die (all outcomes equally likely) is:

3.5

The distribution of grades (letter grade and GPA numerical equivalent value) in a large statistics course is as follows:

A,4.0-0.2; B.3.0- 0.3; C.2.0-0.3; D.1.0- 0.1; F.0.0-

What is the probability of getting an F?

A,4.0-0.2; B.3.0- 0.3; C.2.0-0.3; D.1.0- 0.1; F.0.0-

What is the probability of getting an F?

0.1

The distribution of grades (letter grade and GPA numerical equivalent value) in a large statistics course is as follows:

A,4.0-0.2; B.3.0- 0.3; C.2.0-0.3; D.1.0- 0.1; F.0.0-

What is the expected value?

A,4.0-0.2; B.3.0- 0.3; C.2.0-0.3; D.1.0- 0.1; F.0.0-

What is the expected value?

2.4

On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses 0.25 point for an incorrect answer.

If the student has no idea of the correct answer for a particular question and merely guesses, what is P(getting the correct answer) and P(choosing incorrectly)?

If the student has no idea of the correct answer for a particular question and merely guesses, what is P(getting the correct answer) and P(choosing incorrectly)?

P(correct) = 0.25; P(incorrect) = 0.75

On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses 0.25 point for an incorrect answer.

If the student has no idea of the correct answer for a particular question and merely guesses, what is the student’s expected gain or loss on the question?

If the student has no idea of the correct answer for a particular question and merely guesses, what is the student’s expected gain or loss on the question?

0.0625

Suppose you were using an eight-sided number die that was rigged to have one side occur more than the others (not equally likely). The probability model of the trick die is:

1-0.5; 2-0.2; 3-0.05; 4-0.05; 5-0.05; 6-0.05; 7-0.05; 8-0.05

What is the expected value?

1-0.5; 2-0.2; 3-0.05; 4-0.05; 5-0.05; 6-0.05; 7-0.05; 8-0.05

What is the expected value?

2.55

THE LAW OF LARGE NUMBERS states that the mean outcome in many repetitions gets close to the expected value.

…

Suppose you were using an eight-sided number die that was rigged to have one side occur more than the others (not equally likely). The probability model of the trick die is:

If this die is rolled 6000 times, then the mean of the number of spots actually observed on each of the 6000 rolls should be about:

If this die is rolled 6000 times, then the mean of the number of spots actually observed on each of the 6000 rolls should be about:

2.55

If you do not know the outcome probabilities, you can estimate the expected value by:

Both using the Law of Large Numbers and using simulation

Numbers that describe a population are called:

Parameters

The students in a college statistics class want to estimate what proportion of the students in their college own an iPod. They gather an SRS of 500 students. They find that 187 of the students in the sample own an iPod.

What is the population of interest for this poll?

What is the population of interest for this poll?

The students of the college

A confidence interval:

Tells us how uncertain the estimate is, Gives us a range of plausible values for the parameter, Helps to answer the question, “How good is the statistic as an estimate of the parameter?”

The students in a college statistics class want to estimate what proportion of the students in their college own an iPod. They gather an SRS of 500 students. They find that 187 of the students in the sample own an iPod.

What is the numerical value of the sample proportion,

P^ from the sample?

What is the numerical value of the sample proportion,

P^ from the sample?

0.3740

The students in a college statistics class want to estimate what proportion of the students in their college own an iPod. They gather an SRS of 500 students. They find that 187 of the students in the sample own an iPod.

What is most likely true about the population proportion p in this setting?

What is most likely true about the population proportion p in this setting?

It is approximately 37.4%.

A newspaper poll on state budgetary issues interviewed 828 state residents. Of the residents surveyed, 470 of them felt that the state should balance the budget. Use the poll results to give a 95% confidence interval for p.

0.5332 to 0.6020

A confidence interval for a parameter has:

Both an interval calculated from the data and a confidence level which gives the probability that the interval will capture the true parameter value in repeated samples.

A radio station survey random sample of 495 listeners found that 74 of them had a satellite radio. A 99% confidence interval would be:

0.1081 to 0.1909

A bored statistician begins to flip a coin. He flips the coin 5 times and records the proportion of heads. Then he flips the coin 15 times and records the proportion of heads. Then he flips the coin 30 times and records the number of heads. He begins to see a trend, the more times he flips the coin, the closer he gets to 0.5 heads. This is an example of:

Law of Averages

True or False: 30 male college students have a mean of 170 and a standard deviation of 10. A 95% confidence interval around male college student weight is 150.4 to 189.6.

false