#2 (16 points) Bimble encounters the following problem while studying for her ma
ID: 3350710 • Letter: #
Question
#2 (16 points) Bimble encounters the following problem while studying for her managerial statistics exam. Please answer each of the problems below for her so she can use your answers as her study guide. The problem For itemized tax returns in the $60,000-$75,000 income group for the most recent year reported, the average charitable contribution was $1935. Assume a normal distribution and a standard deviation of $400. a) For a randomly selected household from this income group, what is the probability that the household made charitable contributions of at least $1600? (4) b) For a randomly selected household from this income group what is the probability that the household made charitable contributions of between $2200 and $2400? (4) what level of contributions was exceeded by only 20% of the itemized returns in this income group? (4) c) d) what level ofcon tributions was exceeded by 40% of the itemized returns in this income group? (4)Explanation / Answer
a) P(X>1600)
P(Z > (1600-1935)/400 ) =P(Z > -0.8375) =1- P(Z< -0.8375) = 0.7988
b) P(2200 < X< 2400)
P(2200 < X< 2400) = P( (2200-1935)/ 400 < Z < (2400-1935)/400) = P(0.6625 < Z< 1.1625) =0.8775-0.7462= 0.1313
c) P(X >x) =20% or 0.2
P(X< x) = 1- P(X>x) = 0.8
Z(0.8) =0.842
0.842 = (x- 1935) /400 => x= 2271.8(2272)
d) P(X> x) =40%
P(X<x) = 0.6
Z(0.6)= 0.253
0.253= (x- 1935) /400 =>x= 2036.2 (2036)
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