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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

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=profit ($)4812
P(X)0.180.500.32
Mean:μX=$8.56
Standard deviation:σX≈$2.77
The company is going to run a promotion where customers get $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?
μY=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dollars
σY≈
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dollars