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Expected counts in a goodness-of-fit test

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Problem

A bakery sells cakes, cookies, and pastries. They wonder if customers are equally likely to buy each product. They take a sample of 200 recent purchases and record what was purchased (they are willing to treat this as a random sample). Here are the results:
ProductCakesCookiesPastries
Observed purchases656867
They want to perform a χ2 goodness-of-fit test to determine if these results suggest that one type of product is more popular than the others.
What is the expected count of cake purchases?
You may round your answer to the nearest hundredth.
Expected:
  • 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
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