February 13, 2009 Conditional Probability/Analyzing Data HAPPY FRIDAY THE 13 th !!!!!

REMINDER:  If A and B are mutually exclusive events:  If A and B are not mutually exclusive events

REMEMBER:  Example 1: About 53% of U.S. college students are under 25 years old. About 21% of U.S. college students are over 34 years old. What is the probability that a college student chosen at random is under 25 or over 34?  Example 2: Suppose you reach into a bowl of 3 red apples, 3 green apples, 1 lime, 1 lemon, and 2 oranges. What is the probability that the fruit is an apple or green?

REMEMBER:  : “the probability of the event B, given the event A”  Formula:

 Researchers asked people who exercise regularly whether they jog or walk. Fifty- eight percent of the respondents were male. Twenty percent of all respondents were males who said that they jog. Find the probability that a male respondent jogs.

A student in Buffalo, New York, made the observations below: ◦ Of all snowfalls, 5% are heavy (at least 6 in.) ◦ After a heavy snowfall, schools are closed 67% of the time ◦ After a light snowfall (less than 6 in.) schools are closed 3% of the time. Find the probability that the snowfall is light and the schools are open.

 Look over last night’s homework with the people next to you.  Ask questions and help each other with the problems you struggled with last night.

Analyzing Data

Measures of central tendency help describe a data set  Mean: the average of all the data values  Median: middle value or mean of the two middle values  Mode: the most frequently occurring value

 Find the mean, median, and mode for the following values: 1. 98, 95, 99, 97, 89, 92, 97, 62, , 4.3, 3.7, 3.9, 2.8, 5.4, 2.8

 There are 5 parts to a box and whisker plot: 1. Minimum Value 2. Quartile 1 (Q1): The median of the lower half 3. Quartile 2 (Q2): The median of the entire data set 4. Quartile 3 (Q3): The median of the upper half 5. Maximum Value

Median of the upper part (Q3) = 83 Median of the set of data (Q2) = 72.5 Median of the lower part (Q1) = 83

 Make a box-and-whisker plot for the following values: 84, 79, 90, 73, 95, 88, 92, 81, 67

 Percentile: a number that indicates the percent of data that is less than or equal to a particular number in the data set.  Find the values at the 20 th and 65 th percentiles for the following values: 54, 98, 45, 87, 98, 64, 21, 61, 71, 82, 93, 65, 98, 87, 24, 65, 97, 31, 47

 Step 1: Put the values in numerical order: 21, 24, 31, 45, 47, 54, 61, 62, 64, 65, 65, 71, 82, 87, 87, 93, 97, 98, 98, 98  Step 2: Find the number of values that fall below the 20 th percentile and the number of values that fall below the 65 th percentile

 Find the value at the 0 th percentile of the last data set.  Find the value at the 45 th percentile of the last data set.

 Outlier: An item of a data set with a value substantially different from the rest of the items in the data set.  Find the outlier for this set of values. Describe how it would affect the mean of the data: 56, 65, 73, 59, 98, 65, 59

 Suppose the values in Example 6 are measurements of the water temperature of a lake. Would you discard the outlier? Why?  Suppose the data represent the number of customers in a small restaurant each night during one week. Would you discard the outlier? Why?

 Pg 664 #1, 2, 4, 5, 8-10, 12, 14-17, 19