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Chapter 13 Written Homework Assignment MATH-138 Statistics Directions: On a separate sheet of paper, write out your solutions to the questions below. Then scan your written work, save it as a PDF le, and submit it on Canvas. Late assignments will receive a grade of zero unless prior arrangements are made with me. Assignment: Show all of your work! (35 points total) Sammg Distribution Models for Proportions Consider the following properties of sampling distributions for proportions: - The population distribution of a proportion is bimodal. The sampling distribution of is Normal as long as the sample size is big enough. To meet this condition the sample must have at least IO success and I 0 failures. In other words, and . - The mean of the sampling distribution of is the population proportion. In symbols we write: - The standard deviation of the sampling distribution of is the square root of times divided by . In symbols we write: 1) Use the information above and what you learned from Chapter 5 regarding the normalcdf command to answer the questions below. It is generally believed that nearsightedness affects about 12% of all children. A local elementary school registered 100 incoming kindergarteners. (2 points each) a) Find the mean and standard deviation of the sampling distribution and describe the sampling distribution using the notation . b) What is the probability that less than 10% of the incoming kindergarteners are nearsighted? c) What is the probability that more than 15% of the incoming kindergarteners are nearsighted? d) If this school measures at the 80'h percentile for all incoming kindergarten classes, what proportion of incoming kindergarteners are nearsighted