Question

IV, a food vendor at its Field believes Veggie Burgers ) laste and look exactly the same as hamburgers (). To test this hypothesis, orders 15 veggie burgers and 20 hamburgers for a game. These burgers are m ed together so the chef cannot tell which is Veggle. Suppose burgers are eaten of the game. These are randomly selected from the 25 burgers, Let X - the number of the eaten burgers which are weg Burgers a. How many possible ways are there to select the 7 out of 5 burgersforder does not matter) b. What is the probability that X-2 c. What is the probability that X-17 d. What is the probability that X 37 e. What is the expected value of X7 1. What is the standard deviation of X2 9. What is the probability that is within 1.1 standard deviations of its expected value? h. IF TV gets $130 from the manufacturer for each Veggie Veggie Burger eaten then what is the expected amoun Add any comments below t s from the manufacturer

Answer 1

a) total possible ways = 35C7 = 6724520

b) P(X=2)= C(15,2)*C (20,5)/C(35,7)           =   0.2421

c) P(X=1)= C(15,1)*C (20,6)/C(35,7)           =   0.0865

d) P(X<3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.3401

e)

Sample size,     n =    7
No. of events of interest in population    , k =   15
Population size   , N =   35

expected value= mean = E(X) = n(k/N) =    3

f)

variance = nk(N-k)(N-n)/(N²(N-1)) =    1.4118
  
std dev = √variance =    1.1882
  
g) P(-1.1 <X-µ < 1.1 ) = P(1.9<x<4.1) = P(X=2) + P(X=3) + P(X=4)= 0.8013

h) expected money = 130*3 = $390