Question

please use R if possible to write code and answer the questions.

Suppose I work at a bakery that sells two types of pies: apple and pumpkin. The pies are boxed in such a way that I must open the box to identify what type of pie is inside. I know the probability that a randomly selected pie is an apple pie is 42%. Assume any samples are randomly selected, and assume that I am opening randomly selected boxes. (a) (3 pts) How many boxes should I expect to open before I find an apple pie? (b) (3 pts) I have 27 pies. What is the probability that more than 17 are pumpkin? (c) (3 pts) What is the probability that I must open at least 5 boxes to find apple? (d) (3 pts) I have 32 pies to sell. How many should I expect to be apple? (e) (3 pts) Of the 32 pies, what is the probability that less than 9 are apple? (f) (3 pts) What is the probability that I must open exactly six pies to find pumpkin?

Answer 1

bbu2 umpkin 2=0 Given two types of pies, app Where Do Prapple) = 0.42 L . q-lab - P(Pumpkin) = 0.58. a) Let, x = be the number of box - required to get a bapple box I So, P(X=x) = qto x=0,1,2,- - E(X) = x. qt qa qap - E p { 1 + 294+39 to...? = p (1-9) 11 22 __ ~ 20381 b) Let, ý be the number of pumpking • he gets among 27 pies 27-4 • so, ply=y) = (27) q (1-9) a tofind ply> 17) -- Ply< 172 the Bin (27,0.58 (From R ent e PSX25) = 1- P(x+4) = 0.0656 X~ Geometric (0.42) ( From R we I as in a part a J get d) Now, y~ Bin (32, 0.42) * here Y = # apple among 32 piee - ElY) = 32 x 0.42 (By Rule of Binowe att wawili katika dakika 3 13:44

R code is

#part b
1-pbinom(17,27,0.58)

#part c
1-pgeom(4,0.42)

As per HomeworkLib policy we have permission to answer first 4 sub parts only.