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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 8

Lesson 3: Transforming random variables
Math
AP®︎/College Statistics
Random variables and probability distributions
Transforming random variables
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Transforming random variables

AP.STATS: VAR‑5 (EU), VAR‑5.F (LO), VAR‑5.F.1 (EK)
Google Classroom

Problem

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from each size. Let X represent the shop's profit on a randomly selected pizza. Here's the probability distribution of X along with summary statistics:
SmallMediumLarge
X, equals, start text, p, r, o, f, i, t, space, left parenthesis, dollar sign, right parenthesis, end text4812
P, left parenthesis, X, right parenthesis0, point, 180, point, 500, point, 32
Mean:mu, start subscript, X, end subscript, equals, dollar sign, 8, point, 56
Standard deviation:sigma, start subscript, X, end subscript, approximately equals, dollar sign, 2, point, 77
The company is going to run a promotion where customers get dollar sign, 2 off any size pizza. Assume that the promotion will not change the probability that corresponds to each size. Let Y represent their profit on a randomly selected pizza with this promotion.
What are the mean and standard deviation of Y?
mu, start subscript, Y, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
dollars
sigma, start subscript, Y, end subscript, approximately equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
dollars
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