Do Now Find the standard score (z-score) using the given information Mean=785 Standard deviation=134 Observed Score = 614 z = What percentile is this? 10 th percentile

7.2: Probability Models

Tells us what the possible outcomes are A Probability Model Assigns probabilities to these outcomes Marital StatusNever MarriedMarriedWidowedDivorced Probability

Definition: A probability model for a random phenomenon describes all the possible outcomes and says how to assign probabilities to any collection of outcomes. We sometimes call a collection of outcomes an event.

Probability Rules A. Must be a number between 0 and 1 0 ≤ P(E) ≤ 1 B. The sum of the probabilities of all possible outcomes must be 1 C. The probability that an event does not occur is equal to 1 minus the probability that the event will occur. P(not E) = 1 – P(E) D. If 2 events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.

Example Find the P(not married) a.) using rule C b.) using rule D Marital StatusNever MarriedMarriedWidowedDivorced Probability P(not married) = 1 – P(married) P(not married) = 1 – P(not married) =.445 P(not married) = P(not married) =.445

Example Rolling two dice is a common way to lose money in casinos. There are 36 possible outcomes when we roll two dice and record the up-faces in order (first die, second die). The figure below displays these outcomes. a.) What is the probability of each individual outcome? 1/36 b.) What is the probability that the sum of the dice is 5? P(sum is 5) = 4/36

What about personal probabilities? Personal probabilities should follow the same rules HOWEVER-If they don’t obey the rules, we can’t say that they are “wrong”. All we can conclude is that they don’t make sense and therefore we say that they are incoherent. Complete the following: Pg /

Probability Models for Sampling The sampling distribution of a statistic tells us what values the statistic takes in repeated samples from the population and how often it takes those values. A sampling distribution is essentially assigning probabilities to the values the statistic can take. Because there are usually many possible values, sampling distributions are often described by a density curve such as a normal curve.

Do you lotto??? The sampling distribution represents the results of a sample of 1523 adults who were asked if they bought a lottery ticket in the past year. The normal curve drawn over the histogram is an ideal pattern that describes the results from a very large number of samples. Example

Example- Do you approve of gambling? An opinion poll asks an SRS of 501 teens if they approve of legal gambling. Suppose that 50% of all teens actually approve of legal gambling with a standard deviation of a.) Using the given info, sketch a normal curve. b.) What is the probability that 52% or more will approve? c.) What is the probability that less than 47% will approve? Practice Complete pg /

7.2 Review: pg / Chapter 7 Review pg / ,