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155S6.3.notebook February 22, 2010 Some General Information MAT 155DY1 & DY2 Chapter 6 Normal Probability Distribution 6.3 Applications of Normal Distribution You can find the following two lessons in the Course Documents section of CourseCompass: S3D.1 MAT 155 Chapter 6 Normal Probability Distributions S3D.1.1 MAT 155 Using Technology for Chapter 6 The following are some animations or other media items pertaining to Chapter 6. The items listed to Section 6.2, 6.3, 6.4, and 6.5 may be found in the multimedia section of your course in CourseCompass. Section 6.2 Random Variable X Section 6.3 Pulse Rate Section 6.4 Standard Deviation of Sample Means Section 6.5 Central Limit Theorem Visit Dr. Moore’s website for Excel programs to help solve problems in Chapter 6 Normal Probability Distributions. In Software & Technology Items, scroll down to Mathematical Modeling & Statistics and open Normal Distribution (xls) http://cfcc.edu/faculty/cmoore/S3.159a.6C.NormDist.xls Feb 138:58 PM Section 6.3 Applications of Normal Distribution Using zscore and atable to find probability. Feb 138:58 PM Section 6.3 Applications of Normal Distribution 277/8. Adult IQ scores are normally distribution with mean of 100 and std of 15. Select an adult at random. Draw a graph and find P(110 < IQ < 120). Feb 138:58 PM Feb 138:58 PM Section 6.3 Applications of Normal Distribution 277/6. Adult IQ scores are normally distribution with mean of 100 and std of 15. Select an adult at random. Draw a graph and find P(IQ > 131.5). [requirement for Mensa membership] Feb 138:58 PM Section 6.3 Applications of Normal Distribution 277/10. Adult IQ scores are normally distribution with mean of 100 and std of 15. Draw the graph and find the IQ score that separates the bottom 60% from the top 40%. Feb 138:58 PM 1 155S6.3.notebook Section 6.3 Applications of Normal Distribution 277/12. Adult IQ scores are normally distribution with mean of 100 and std of 15. Draw the graph and find the IQ score that separates the top 85% from the others. Feb 138:58 PM Section 6.3 Applications of Normal Distribution 278/16. Men’s and women’s heights are normally distributed. Men: mean 69.0 in. and std 2.8 in. Women: mean 63.6 in. and std 2.5 in. The standard casket has inside length of 78 in. (a) What percentage of men are too tall? Of women? Standard size adequate? Feb 138:58 PM Section 6.3 Applications of Normal Distribution 278/18. Birth weights in Norway are normally distributed with mean of 3570 g and std of 500 g. What weight should be used to separate the lightest 2% from the others? Feb 138:58 PM February 22, 2010 Section 6.3 Applications of Normal Distribution 278/14. Women’s heights are normally distributed with mean 63.6 in. and std 2.5 in. U.S. Army requires women’s heights between 58 in. and 80 in. Find percentage of women meeting this requirement. Are many women being denied admission because of this requirement? Feb 138:58 PM Section 6.3 Applications of Normal Distribution 278/16. (continued) Men’s and women’s heights are normally distributed. Men: mean 69.0 in. and std 2.8 in. Women: mean 63.6 in. and std 2.5 in. The standard casket has inside length of 78 in. (b) What inside length would fit all men except the tallest 1%? Feb 138:58 PM Section 6.3 Applications of Normal Distribution 278/21. Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Wife claimed to birth 308 days after a brief visit from sailor husband. Find probability of pregnancy lasting 308 days or longer. What does the result suggest? (b) Stipulate that a bay is premature if pregnancy is in the lowest 4%, find the length that separates premature babies from others. Feb 138:58 PM 2