## ujuge321 3 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?

1. benice

Is this a poisson distribution?

2. ujuge321

yep

3. benice

i'm not sure on this. @callisto

4. ujuge321

ok

5. benice

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

no it is 0.22

7. benice

how did you get that?

8. ujuge321

i did not get it. That is the answer.

9. benice

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

10. benice

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

11. ujuge321

okay. Thanks.

12. benice

can you do it using the a possion dist?

13. ujuge321

how??

14. benice

we have to decide what alpha is first

15. ujuge321

hmm... i see.

16. benice

the average for the whole population is the same as the unknown small sample ie 12

17. ujuge321

i know that part. but how should we figure out?

18. benice

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

how did you get 20/46?

20. benice

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

ok.

22. benice

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

so we worked out alpha = 5.2173913 and x=5

24. benice

25. ujuge321

0.6160?

26. ujuge321

this question is tough.

27. benice

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

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

goodnight

30. ujuge321

ok. good night