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Download Statistics_A4_NormalCDFv3 - 2011-01-Kelvin
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A4 Statistics – Normal Distribution Functions Mr. Nguyen Grade 11 Applied Math Kelvin High School 1. A teacher is analyzing the class results for three math tests. Each set of marks is normally distributed. Test 1 2 3 Test 1 2 3 Mean 77 83 77 Std. Dev 3.9 3.9 7.4 Oliver’s mark Mean + 2(Std. Dev) Mean – 1(Std. Dev) Mean + 3(Std. Dev) a. Sketch normal curves for tests 1 and 2 on one graph b. Sketch normal curves for tests 1 and 3 on a different graph. Examine your graphs. How do tests 1 and 3 compare? How do tests 1 and 2 compare? c. Determine Oliver’s marks on each test, given the information shown below Grade 11 Applied Math Kelvin High School A4 Statistics – Normal Distribution Functions Mr. Nguyen 2. A school of 130 bottlenose dolphins is living in a protected environment. The life expectancy of the dolphins is normally distributed, with a mean of 39 years and a standard deviation of 3.5 years. How many of these dolphins can be expected to live more than 46 years? 3. A teacher finds that the results on a final exam are normally distributed with a mean of 62 and a standard deviation of 12. a. If the passing grade is 50%, what percent of the class will fail? b. There are 32 students in the class, how many students will receive an A (a mark between 80%-90%) c. How is the question in part b similar to the question in part a? How are they different? 4. The data below shows the reviews for movies currently playing in theatres (1 to 5 stars) Score 0 1 2 3 4 5 Freq. 0 3 5 8 4 2 a. Sketch a graph of this data and decide whether it resembles a normal distribution b. Determine the mean and standard deviation. Do these values validate your answer to part a
