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Download File - Grade 11 Applied Mathematics
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A4 Statistics – Normal Distribution Functions Mr. Nguyen Grade 11 Applied Math Kelvin High School 1. 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? 2. A teacher is analyzing the class results for three math tests. Each set of marks is normally distributed. Test 1 2 3 Mean 77 83 77 Std. Dev 3.9 3.9 7.4 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? A4 Statistics – Normal Distribution Functions Mr. Nguyen Grade 11 Applied Math Kelvin High School c. Determine Oliver’s marks on each test, given the information shown below Oliver’s mark Mean + 2(Std. Dev) Mean – 1(Std. Dev) Mean + 3(Std. Dev) Test 1 2 3 3. 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? 4. The data below shows the reviews for movies currently playing in theatres (1 to 5 stars) Score Freq. 0 stars 0 1 star 3 2 stars 5 3 stars 8 4 stars 4 5 stars 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
