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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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?

Mathematics
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Is this a poisson distribution?
yep
i'm not sure on this. @callisto

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Other answers:

ok
if it uniform all prices are equally likely. so the prob of one store charging less than 3.00 is 20 out 46
no it is 0.22
how did you get that?
i did not get it. That is the answer.
so now it a bionomial which is very similar to the poission dist. 12C5*(20/46)^5*(26/46)^7
http://www.wolframalpha.com/input/?i=%2820%2F46%29%5E5*%2826%2F46%29%5E7*12choose5 according to wolfram is .22267
okay. Thanks.
can you do it using the a possion dist?
how??
we have to decide what alpha is first
hmm... i see.
the average for the whole population is the same as the unknown small sample ie 12
i know that part. but how should we figure out?
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
how did you get 20/46?
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
ok.
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
so we worked out alpha = 5.2173913 and x=5
sub into the possion equation and post your answer
0.6160?
this question is tough.
http://www.wolframalpha.com/input/?i=5.2173913%5E5*exp%28-5.2173913%29%2F5%21 this gives the answer as 0.1746633
which like we said earlier the possion dist is like bionomial.... in that its an estimate.. the possion dist works better for large numbers
goodnight
ok. good night

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