A farm and garden supply store sells fertilizer in 50 pound

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. Find the probability that a random customer buys more than 2 bags. Find the expected value of bags bought. Find the standard deviation of the number of bags bought. Suppose two independent random customers are selected. Find the probability that they each buy 1 bag. Suppose two independent random customers are selected. Find the probability that the total number of bags purchased is at least 8.

Solution

1)

P(more than 2) = P(3) + P(4) + P(5) = 0.12 + 0.06 + 0.02 = 0.20 [answer]

2)

Consider the table:

Thus,          
          
E(x) =    1.85 [ANSWER, EXPECTED VALUE]

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C)

Var(x) = E(x^2) - E(x)^2 =    0.9675      
s(x) =    0.983615779 [ANSWER, STANDARD DEVIATION]

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D)

P(both buy 1 bag) = 0.45*0.45 = 0.2025 [answer]

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E)

P(Total of 8) = P(3) P(5) + P(4) P(4) + P(5) P(3) = 0.12*0.02 + 0.06*0.06 + 0.02*0.12 = 0.0084 [ANSWER]
          

x	P(x)	x P(x)	x^2 P(x)
1	0.45	0.45	0.45
2	0.35	0.7	1.4
3	0.12	0.36	1.08
4	0.06	0.24	0.96
5	0.02	0.1	0.5