SOLUTION: The distribution of the amount of money undergraduate students spend on books for a term is Normal with a mean of $450 and a standard deviation of $80. a) If a student is select

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Question 873321: The distribution of the amount of money undergraduate students spend on books for a term is Normal with a mean of $450 and a standard deviation of $80.
a) If a student is selected at random, what is the probability that this student spends more than $470 on books in a term?
b) If an SRS of 100 undergraduates is selected, what is the probability that their average amount of money spent on books this term is more than $470?
c) 99% of students spend between ____ and ____ dollars on textbooks.
d) If an SRS of 100 undergraduates is measured, 99% of the time the average will fall between ____ and _____ dollars.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

a) P( z > 20/80) = P(z > .25) = .4013  0r 40.13% chance

b) P( z > 20/80/sqrt(100)) = P(z > 20/8) = P(x > 2.5) = .0062  Or .62% chance

c) z < invNorm(.995) = 2.576 = (X - 450)/80 = 80*2.576 + 450 = 206 + 450 = 656

   z < invNorm(.005) = 80(-2.576) + 450 = -206 + 450 = 244

99% of students spend between $244 and $656 dollars on textbooks. 

d)  z < invNorm(.995) = 2.576 = (X - 450)/80/sqrt(100) = 20.6 + 450 = $470.60

    z < invNorm(.005) = 8(-2.576) + 450 = -20.6 + 450 = $429.40

99% of students spend between $429.40 and $470.60 dollars on textbooks.