IM 4 SS: BOOK 2B UNIT 7 TEST
Review: Standard Deviation and Normal DistributionsName:___________________________ #______Part I: For each question in this section you should be using the approximations of the empirical rule to find your answer. Do not use the z-score table. Show work when applicable.1. Use the diagram below to answer the questions to the right.a) What is the mean of the data set?b) What is the standard deviation of the data set?2. As part of a study on the diet of polar bears, 250 polar bears are randomly chosen and their weights are taken. The distribution of the weights is approximately normal. The average weight is 712 pounds and the standard deviation is 23 pounds.a) Sketch a normal curve with an appropriate scale on the horizontal axis.b) Approximately what percent of polar bears fall between weights of 643 and 735 pounds?c) Approximately what percent of polar bears have a weight less than or equal to 666 pounds or more than 781 pounds?d) Approximately how many polar bears have a weight between 712 and 758 pounds?Part II: For each question in this section you should be using the z-score table. Show work.3. The scores on a history quiz are approximately normal. The mean and standard deviation on the quiz are μ= 65 and σ=17. Find the z-scores for the student below. Show your work. Explain what the z-score tells you about the student’s score with respect to their classmates. Be specific.Catherine scored 73. Z-score:Meaning:4. The scores on a recent political science quiz are approximately normal. The mean and standard deviation on the quiz are μ= 72 and σ=7.4. Find the test scores corresponding to the z-score for the student below. Show your work.Erica z-score was -1.05. 5. A track coach enjoys making her athletes think. She decided not to tell her athletes how fast they ran their 400 meter event in practice. The athletes times were distributed normally and had a mean and standard deviation as follows μ= 56 seconds and σ=4.5 seconds. a) Help Serach find his time if he is in the 71st percentile. Show and explain your work.b) Help Fere find her time if she is in the 55th percentile. Show and explain your work.6. Ms. Latham is considering curving your quiz scores which were approximately normally distributed and originally had a mean and standard deviation of μ= 65 and σ=12.5. She plans to change the mean to 72 and the standard deviation to 8 points.a) What would an original score of 48 become once the grades were curved? Show your work. Would you support the teacher curving the grades? Support your answer with what you’ve learned about standardizing scores.b) Suppose you made a score of 90 on the quiz. Would you support the teacher curving the grades? Support your answer with what you’ve learned about standardizing scores.7. Heights for Disney Princesses at Disney World are approximately normally distributed with mean of 5 ft 4 inches and a standard deviation of 3 inches.a) What percentage of princesses have a height less than or equal to 5 feet or greater than 5 feet 6 inches? Explain how you obtained your answer.b) Find the height of the princesses who are in the 15th percentile.c) Tinkerbell is 4 feet 11 inches, while Belle is 5 ft 8 inches. What percent of Disney Princesses fall between Tinkerbell and Belle’s heights? ................
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