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MATH 17282-Suppose that 20% of the adult women in the

Suppose that 20% of the adult women in theUnited States dye or highlight their hair. Wewould like to know the probability that a SRS ofsize 200 would come within plus or minus 3percentage points of this true value. In otherwords, find probability that ˆp takes a valuebetween 0.17 and 0.23Use the following to answer questions 12 – 13: The high temperature in Chicago for the month of August isapproximately normally distributed with mean ? = 80 F and standard deviation = 8 F. Suppose we takea SRS of 16 days in August and want to determine the sample mean, ¯x high temperature.12. What is the standard deviation (standard error) of the sample mean high temperature.a. 8b. 2c. 0.5d. 10e. 2013. What is the probability that a random sample of 16 days in August have a sample mean high temperatureof at least 82 F?a. 0.5987b. 0.2500c. 0.1587d. 0.8413e. Cannot be determined.3. If a distribution has a mean of 48 and standard deviation of 3.2, what is the value that corresponds toa z-score of -1.6?a. 38.22b. 42.88c. 53.12d. 46.40e. none of these

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