2.2 Standard Normal Calculations, cont.

Because all Normal distributions are the same once we standardize, we can find percentages under Normal curves without Calculus by using the standard Normal table. Recall: an area under a density curve is a proportion of the observations in a distribution.

Using the Standard Normal Table Find the proportion of observations from the standard Normal distribution that are less than 2.22.

Using the Standard Normal Table Find the proportion of observations from the standard Normal distribution that are greater than

Be aware... A common mistake is to look up a z-value in Table A and report the entry corresponding to that z-value, regardless of whether the problem asks for the area to the left or to the right of that z-value. Always sketch the standard Normal curve, mark the z- value, shade the area of interest, and make sure your answer is reasonable in the context of the problem.

Cholesterol in Young Boys For 14-year-old boys, the mean is µ =170 milligrams of cholesterol per deciliter of blood (mg/dl) and the standard deviation is σ =30 mg/dl. Levels above 240 mg/dl may require medical attention. What percent of 14-year-old boys have more than 240 mg/dl of cholesterol?

Cholesterol in Young Boys What percent of 14-year-old boys have blood cholesterol between 170 and 240 mg/dl?

SAT Verbal scores Scores on the SAT Verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? Previous problems asked for a proportion of observations satisfying some condition. This problem gives us the proportion and asks us to find the observed value.

Assessing Normality Normal distributions are important because they provide good models for many real life data sets: gas mileage of 2006 Corvette convertibles, statewide unemployment rates, and weights of 9-ounce bags of potato chips. But keep in mind - you can only use these calculations and Table A if the data is Normal!