NORMAL DISTRIBUTIONS Chapter 11 1 Objectives Calculate probabilities

NORMAL DISTRIBUTIONS Chapter 11. 1

Objectives: Calculate probabilities using normal distributions Previously we learned you describe density curves according to SOCS • Shape (right skewed, left skewed, symmetrical) • Outliers • Center (mean or median) • Spread (standard deviation or IQR) We will now look at a special density curve called the Normal Distribution.

The graph of a normal distribution is a bellshaped curve called a normal curve that is symmetric about the mean. The areas under a normal curve can be interpreted as probabilities in a normal distribution. Data can be more than 3 standard deviations from the mean but we typically won’t measure that far out. The idea of certain percentages of data falling within a certain number of standard deviations from the mean is often referred to as the 68 -95 -99. 7 Rule.

The scores for a state’s peace officer standards and training test are normally distributed (follows the 68 -95 -99. 7 rule) with a mean of 55 and a standard deviation of 12. The test scores range from 0 to 100. a. About what percent of the people taking the test have scores between 43 and 67?

An agency in the state will only hire applicants with tests scores of 67 or greater. About what percent of the people have test scores that make them eligible to be hired by the agency? or, 50% of the applicants score above 55, 34% fall one standard deviation to the right, so 50 – 34 = 16%

Suppose that the data concerning the first-year salaries of Barush (a college in NYC) graduates is normally distributed with the population mean µ = $60000 and the population standard deviation σ = $15000. Find the probability of a randomly selected Baruch graduate earning less than $30000 annually. To answer this question, we have to find the portion of the area under the normal curve from 30 all the way to the left. 13. 5% 34% 15 30 45 60 75 salary in 1000’s 90 105

What percent of the graduates will make between $45000 and $90000? 34% + 13. 5% = 81. 5% of the graduates will make between 45 and 90 thousand dollars. 15 30 45 60 75 salary in 1000’s 90 105

What is the probability that you randomly select someone who makes either more than$105, 000 or less than $15, 000? 15 30 45 60 75 salary in 1000’s 90 105 0. 15 + 0. 15 = 0. 30. There is a 0. 30% chance of randomly selecting a recent graduate who makes more than $105, 000 or less than $15, 000

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