1. A farm and garden supply store sells fertilizer in 50 pound bags. For each cu
ID: 3307413 • Letter: 1
Question
1. A farm and garden supply store sells fertilizer in 50 pound bags. For each customer purchasing fertilizer the probability distribution for the number of bags purchased is given below.
e. Find the expected value of bags bought.
f. Find the standard deviation of the number of bags bought.
g. Suppose two independent random customers are selected. Find the probability that they each buy 1 bag.
h. Suppose two independent random customers are selected. Find the probability that the total number of bags purchased is at least 8.
Prob 0.26 0.29 0.20 0.18 0.07 BagsExplanation / Answer
e. E(X) = 1*0.26 + 2*0.29 + 3*0.20 + 4*0.18 + 5*0.07 = 2.51
f. V(X) = 1*0.26 + 4*0.29 + 9*0.20 + 16*0.18 + 25*0.07 - 2.51*2.51 = 1.55
Standard deviation = 1.55 = 1.245.
g. Probability that one customer buys 1 bag = 0.26
=> Probabillity that both customers buy 1 bag = 0.26 * 0.26 = 0.0676
h. The total number can be atleast 8 if the number of bags bought are (3,5),(4,4),(4,5),(5,3),(5,4),(5,5).
Their probabilities are 0.20*0.07 + 0.18*0.18 + 0.18*0.07 + 0.07*0.20 + 0.07*0.18 + 0.07*0.07 = 0.0905.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.