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ujuge321

  • 2 years ago

The regular retail price of a particular box of a well-known brand of cereal ranges from $2.80 to $3.25 across the grocery stores in the city. The distribution of the prices follows a uniform distribution. If 12 stores are selected at random and the regular retail price of the cereal is recorded, what is the probability exactly 5 of the stores charge less than $3.00?

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  1. benice
    • 2 years ago
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    Is this a poisson distribution?

  2. ujuge321
    • 2 years ago
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    yep

  3. benice
    • 2 years ago
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    i'm not sure on this. @callisto

  4. ujuge321
    • 2 years ago
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    ok

  5. benice
    • 2 years ago
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    if it uniform all prices are equally likely. so the prob of one store charging less than 3.00 is 20 out 46

  6. ujuge321
    • 2 years ago
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    no it is 0.22

  7. benice
    • 2 years ago
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    how did you get that?

  8. ujuge321
    • 2 years ago
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    i did not get it. That is the answer.

  9. benice
    • 2 years ago
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    so now it a bionomial which is very similar to the poission dist. 12C5*(20/46)^5*(26/46)^7

  10. benice
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=%2820%2F46%29%5E5*%2826%2F46%29%5E7*12choose5 according to wolfram is .22267

  11. ujuge321
    • 2 years ago
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    okay. Thanks.

  12. benice
    • 2 years ago
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    can you do it using the a possion dist?

  13. ujuge321
    • 2 years ago
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    how??

  14. benice
    • 2 years ago
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    we have to decide what alpha is first

  15. ujuge321
    • 2 years ago
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    hmm... i see.

  16. benice
    • 2 years ago
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    the average for the whole population is the same as the unknown small sample ie 12

  17. ujuge321
    • 2 years ago
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    i know that part. but how should we figure out?

  18. benice
    • 2 years ago
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    ahh for example if i said half the shops were less than average.. 12*.5=6 then alpha would be 6 but were dealing with 3.00 so its 20/46 12*(20/46)=5.2173913 so ALPHA is 5.2173913

  19. ujuge321
    • 2 years ago
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    how did you get 20/46?

  20. benice
    • 2 years ago
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    pick a number between 0 and 5 ... there is 6 choices even though 5-0=5 so with 3.25-2.80=45cents there is 46 choices now less than $3 is 2.99 to 2.80 2.99-2.80=20 choices so prob(x<$3)=20/46

  21. ujuge321
    • 2 years ago
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    ok.

  22. benice
    • 2 years ago
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    what uniform is saying is every price has the same prob of occuring P(x=2.80)=P(x=2.81)=....................................=P(x=3.25) so 46 equal likely probs which all add to 1 1/46 is there prob individually

  23. benice
    • 2 years ago
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    so we worked out alpha = 5.2173913 and x=5

  24. benice
    • 2 years ago
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    sub into the possion equation and post your answer

  25. ujuge321
    • 2 years ago
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    0.6160?

  26. ujuge321
    • 2 years ago
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    this question is tough.

  27. benice
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=5.2173913%5E5*exp%28-5.2173913%29%2F5%21 this gives the answer as 0.1746633

  28. benice
    • 2 years ago
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    which like we said earlier the possion dist is like bionomial.... in that its an estimate.. the possion dist works better for large numbers

  29. benice
    • 2 years ago
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    goodnight

  30. ujuge321
    • 2 years ago
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    ok. good night

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