Warmup Normal Distributions

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Presentation transcript:

Warmup Normal Distributions The height of adult females is distributed N(64, 2.5). Use the 68-95-99.7 rule to find the percentage of females between 59 and 71.5 inches What proportion of females are between 60 and 66 inches? Normal Distributions

Section 2.2 Normal Distributions Learning Objectives After this section, you should be able to… DESCRIBE and APPLY the 68-95-99.7 Rule DESCRIBE the standard Normal Distribution PERFORM Normal distribution calculations ASSESS Normality

Using the Calculator Normal Distributions Example: To find the proportion of values within a range for a Normal distribution: Home -> Add Calculator Menu -> 5 Probability -> 5 Distributions -> 2 Normal CDF If it is a “less than” question, leave Lower Bound as is and put value in Upper Bound If it is a “greater than” question, put value in Lower Bound and a few 9’s in Upper Bound Example: The height of adult females is distributed N(64, 2.5). What proportion of females are between 60 and 66 inches? What proportion of females are shorter than 68 inches? What proportion of females are taller than 60 inches?

Using Table A backwards Normal Distributions Human pregnancies have a distribution N(266, 16). How many days do the shortest 30% of pregnancies last? Find the closest value in the body of the table to the decimal equivalent of the percentage Determine the corresponding z-score Use the z-score formula to find x Example #1 How many days do the shortest 30% of pregnancies last? How many days do the longest 12% of pregnancies last?

Using Table A backwards Normal Distributions Example #2 The height of adult males is N(69, 3). a) How tall is a male to be in the shortest 60%? b) What are the range of heights to be in the middle 50%?