0 Question 17 v Recall that the CLT states that if you take repeated samples of size n from a population, regardless of whether or not it is normally distributed, then as Long as n > 30 the resulting sampling distribution for i will be normally distributed with: 0' pjzpandoiz WI The standard deviation formula above is used in the margin of error formula for a Z-interval for a population mean. A similar result is that if you take repeated samples from a binomial distribution, then as Long as n is large enough that there are at least 5 successes and 5 failures then the resulting sampling distribution for p' will be normally distributed with: P"? pp'2pand0'p': n . Here, p is the "population proportion" and p' is the "sample proportion". You should recognize the standard deviation formula above as part of the margin of error formula for a Z- interval for a population proportion. Now, suppose that 13% of a population has a virus. Find the probability that if you take a random sample of 120 members of this population, over 17% have the virus. In other words, assuming thatp = 0.13, find P[p' > 0.17). You can use the normalcdf command, with the mean and standard deviation from the formulas above. 0 Question 18 v A random sample of 93 American female soccer players found that 15 play professionally abroad. Build a 89% CI for the proportion of American female soccer players that play abroad. This will be a Z-lnterval since it involves a proportion. A x The formula for the sample proportion is: p = . Round to three decimals. n ago: To find the Margin of Error, E, we need to find the Critical Value, Z6. To do this we use invNorm(C + (1- CH2}, where in this problem 0 = 0.89. Round to three decimals. b. Z6: - n Next we find the Margin of Error: E = ZC - \\/ . Remember that Q = 1 g3 Round to three decimals. c.E= Finally, we compute our Cl: g3 E a: p ~