Question

3. Lucas is the world's WORST sno cone maker. He drops 78% of the snow cones he makes. It's a terrible waste of sno. Anyway, his managers are fed up and start to collect data. They watch Lucas make a sample of 20 sno cones. a. What is the probability that the sample will contain 12 dropped sno cones? b. What is the probability that the sample will contain no good sno cones- i.e. he drops them all? c. What is the probability that the sample will contain less than 8 dropped sno cones? d. What is the probability that the sample will contain at least 15 dropped sno cones?

Answer 1

Let X = no. of dropped Sno cones. Then X-Binomial 20,0.78). (a) P(X = 12) = 0.0351 (R code: round(dbinom(12,20,0.78), 4)). (6) P(X = 20) = 0.0069 (R code: round(dbinom(20,20, 0.78), 4)). (C) P(X<8) = P(X < 7) = 0.0000 (R code: round(pbinom (7,20,0.78), 4)). (d) P(X > 15) = 1 - P(X < 14) = 0.7343 (R code: round(1 - pbinom(14, 20,0.78), 4)).