# Continuous Probability Distribution_ The Normal Distribution Report_ Georgia Tselikis.pdf

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oiU7: Summative Assessment Georgia Tselikis 17 May, 2021 Knowledge and Application Answer the following questions using the z-score chart or by using a spreadsheet. (Each question or portion of a question is worth 2 marks a piece) Total Score /16 Let “p” represent percentile. 1. Find the z-score for x = 8 if the mean is 7 and the standard deviation is 2. 2. Find the percentile for x = 8 if the mean is 7 and the standard deviation is 2. it is the 69th percentile. 3. For a mean of 20 and standard deviation of 5, find p(x<=17) . 4. For a mean of 75 and a standard deviation of 3, find .
5. For a mean of 153 and standard deviation of 25, find . 6. IQ scores of people around the World are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius?
7. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg?
b. A car is said to be in the 90th percentile. How much does it weigh?
Application, Thinking, and Communication 1. Using the Statistics for 42 Countries , choose one variable to collect for each of the countries. You may use the data you have collected in the past. Calculate the percentile of the country for the collected variable by first calculating the mean, standard deviation and z-score. If you sort the countries by the variable from highest to lowest, what percent of the countries are below the chosen country? How does this (actual rank) compare to the percentile calculated with the z-score? Why might the difference have occurred?
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