
Mish L.
asked 02/18/22Suppose 2% of students drink more than 3 cups of coffee each day.
Suppose 2% of students drink more than 3 cups of coffee each day. To check this claim, a researcher randomly selected a sample of 131 students and found that 4 drink more than 3 cups of coffee each day. What is the sampling distribution of the sample proportion? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.)
The distribution of the sample proportion of students drinking more than 3 cups of coffee each day _____(b1) with a mean of _______ and a standard deviation of _______.
(b1) options: (is approximately normal) or (may not be normal)
1 Expert Answer

Jon S. answered 02/18/22
Patient and Knowledgeable Math and English Tutor
distribution of sample proportion: mean is population proportion: 0.02, standard deviation is sqrt(p * (1-p)/n) = sqrt(0.02 * 0.98/131) = 0.01.
because np < 10, the distribution of the sample proportion may not be normal
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David B.
AND because np<10. (some texts use npq<10 others np<=5 or nq<=5) then the normal approximation should not be used in the first place. Use binomial distribution with p = .031 and n = 131. Forget the normal parameters for the sample. note: your estimates for the normal approximation are also false, regardless of having failed the plausible use test. A reasonable approximation to B(n, p) is given by the normal distribution N (np, np(1-p). ( in this case mean = 4 and variance = 3.877) But this is an unreasonable model as p is so small.02/22/22