Question

that is based on a random sample of 235 college graduates. An article stated, "Surveys tell us that more than half of America's college graduates are avid readers of mystery novels." Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion (a) If p = 0.5, what are the mean value and standard deviation of p? (Round your answers to four decimal places.) mean standard deviation If p = 0.6, what are the mean value and standard deviation of p? (Round your answers to four decimal places.) mean standard deviation Does P have approximately a normal distribution in both cases? Explain. Yes, because in both cases np > 10 and n(1-P) > 10. No, because in both cases np < 10 or n(1-P) < 10. No, because when p = 0.5, np < 10. No, because when p = 0.6, np < 10. (b) Calculate PCP 0.6) for p = 0.5. (Round your answer to four decimal places.) Calculate PCP 2 0.6) for p = 0.6. (c) Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 410 rather than 235? When p = 0.5, the PCP 2 0.6) would remain the same if the sample size was 410 rather than 235. When p = 0.6, the PCP 2 0.6) would remain the same if the sample size was 410 rather than 235. When p = 0.5, the PCP 2 0.6) would decrease if the sample size was 410 rather than 235. When p = 0.6, the PCP 2 0.6) would remain the same if the sample size was 410 rather than 235. When p = 0.5, the PCP = 0.6) would decrease if the sample size was 410 rather than 235. When p = 0.6, the PCP = 0.6) would decrease if the sample size was 410 rather than 235. When p = 0.5, the PCP 0.6) would remain the same if the sample size was 410 rather than 235. When p = 0.6, the PCP = 0.6) would decrease if the sample size was 410 rather than 235.

Answer 1

na 235, p=0.5 Mean p=0.5 S.D= Lea 10.500.5 - v ñ - V 235 -0.0326 - b p= 0.6 - Mean a proib S.D= Pq- 0.6x0.4 -0.0320 u ñ u 235 for p=0.5 PL 67,016) - pl 6-km 2 0,6-0,5 L0.0326 =fl 23,3.07) = 1- PL2<3.07) = -0.9989 = 0.0011. for p =0.6 - Plz,0.6) = P p p > 0.6-0.6) . 0.0320) =p270) = 0.5 -