Round to 3 Decimal Places. Everything must be labeled. A farm and garden supply
ID: 3043765 • Letter: R
Question
Round to 3 Decimal Places. Everything must be labeled.
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. 1. Prob 0.38 0.22 Bags 0.15 0.05 4 a. Find the probability that a random customer buys exactly 3 bags b. Find the probability that a random customer buys more than 2 bags c. Find the probability that a random customer buys at least 2 bags d. Find the probability that a random customer buys less than 2 bags e. Find the probability that a random customer buys at most 2 bags f. Find the expected value (mean) of bags bought. g. Find the standard deviation of the number of bags bought. h. Find the probability that the number of bags bought is within one standard deviation of the mean i. Suppose two independent random customers are selected. Find the probability that they each buy 1 bag. j Suppose two independent random customers are selected. Find the probability that the total number of bags purchased is at most 3.Explanation / Answer
a) P(exactly 3 bags) = 1 - (0.38+0.22+0.15+0.05)
= 0.200
b) P(more than 2 bags) = 0.20+0.15+0.05
= 0.040
c) P(at least 2 bags)= 1 - P(1)
= 1 - 0.38
= 0.620
d) P(less than 2 bags) = P(1)
= 0.380
e) P(at most 2 bags) = P(1) + P(2)
= 0.38 + 0.22
= 0.600
f) Expected number of bags = 1x0.38 + 2x0.22 + 3x0.2 + 4x0.15 + 5x0.05
= 2.270
g) Standard deviation of number of bags = [(1-2.27)2x0.38 + (2-2.27)2x0.22 + (3-2.27)2x0.2 + (4-2.27)2x0.15 + (5-2.27)2x0.05](1/2) / 5
= 0.558
h) P(within 1 standard deviation of mean) = P(1.712 <X < 2.828)
= P(2)
= 0.220
i) P(each buy 1 bag) = 0.38*0.38
= 0.144
j) P(both purchase at most 3) = [P(at most 3)]2
= (0.38+0.22+0.2)2
= 0.640
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