How would you solve this stat problem without the calculator?

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Hi my teacher only teaches us how to solve things with a calculator but I want to know how to solve this by hand. I used the normal cdf for this question-An SRS of 400 American adults is asked, "What do you think is the most serious problem facing our schools?" Suppose that in fact 30% of all adults would answer drugs if asked this question. The proportion p-hat of the sample who answer drugs will vary in repeated sampling. In fact, we can assign probabilities to values of p-hat using the normal density curve with mean 0.3 and standard deviation 0.023. Use this density curve to find the probabilities of the following events:a) At least half of the sample believes that drugs are the schools' most serious problem.b) Less than 25% of the sample believes that drugs are the most serious problem.c) The sample proportion is between 0.25 and 0.35. and got-a) normalcdf(0.5,1,0.3,0.023)=1.7^-18b) normalcdf(0,0.25,0.3,0.023)=0.015c) normalcdf(0.25,0.35,0.3,0.23)=0.97How would you solve this by hand? I read that you have to use the z score and so on but could someone show me how?Thank You

Brandyn Moore PhD · Accepted Answer

a) At least half of the sample believes that drugs are the schools' most serious problem. normalcdf(0.5,1,0.3,0.023)=1.7^-18P(X ≥ 0.5) = P((X - 0.3)/0.023 ≥ (0.5 - 0.3)/0.023) = P(Z ≥ 8.69) = P(Z ≤ - 8.69) = 0b) normalcdf(0,0.25,0.3,0.023)=0.015P(X ≤ 0.25) = P((X - 0.3)/0.023 ≤ (0.25 - 0.3)/0.023) = P(Z ≤ - 2.17) = 0.015003c)The sample proportion is between 0.25 and 0.35. P(0.25 ≤ X ≤ 0.35) = P((0.25 - 0.3)/0.023 ≤ (X - 0.3)/0.023 ≤ (0.35 - 0.3)/0.023) = P( - 2.17 ≤ Z ≤ 2.17) = P(Z ≤ 2.17) - P(Z ≤ - 2.17) = 0.984997 - 0.015003 = 0.969994

Mr. Frankie Stiedemann

How would you solve this stat problem without the calculator?

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