Question

15) An eager but misguided statistics professor comes to class one day with 13 slices of bread, a knife, and a large jar of peanut butter. The professor distributes all of the bread to his students, generously smearing peanut butter on one side of each slice. He then instructs his students to toss their slices vigorously into the air. (One slice sticks to the ceiling, and may be ignored in our computations.) or the 12 slices that do fall to the floor, however, calculate the probability that exactly 5 of them will fall peanut butter-side-down. Assume that 60% of all slices will fall peanut butter-side-down in the long run, and that they never land on their edges. What is the mean and standard deviation of this distribution? Find the probability that all 12 of them land peanut butter-side-up. Find the probability that at least one of the 12 slices lands peanut butter-side-up. Find the minimum sample size necessary to estimate the true percentage that will land peanut butter side down to within 4% with 95% confidence if we assume the 60% figure is pretty reliable. We try this with 400 pieces of bread and 264 of them land peanut-butter side down. Estimate the population proportion with a 95% confidence interval. Assume the 60% figure: what is the probability that in a sample of 400, the proportion landing down > .667

Answer 1

Sdlutan o) Qinompdt (12, 6,5)- 0.100a = 10.09% np (12) 6) = 7.2 Mean SD Sxt (np) - sqat (12)(.6)j 2 1-7 C) (.4) .0o0017 P(x-o)= 1- .612- 0.998 d Ptx e) n 2/e (1.96) (1-7)7 0. 4)69.392appox- 70 ) p+-2 /2*gqst (P-Pn) - 0.66+ 1.96 St (Co-66)o-34)/H00 = 6-66+-1.96* Sqzt (o.000561) 0.GG-1.96* o.024 0.6G+-0 O470H -o.61296to o-7070