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The regular retail price of a particular box of a wellknown 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?
 2 years ago
 2 years ago
The regular retail price of a particular box of a wellknown 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?
 2 years ago
 2 years ago

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beniceBest ResponseYou've already chosen the best response.2
Is this a poisson distribution?
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
i'm not sure on this. @callisto
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
if it uniform all prices are equally likely. so the prob of one store charging less than 3.00 is 20 out 46
 2 years ago

ujuge321Best ResponseYou've already chosen the best response.0
i did not get it. That is the answer.
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
so now it a bionomial which is very similar to the poission dist. 12C5*(20/46)^5*(26/46)^7
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=%2820%2F46%29%5E5*%2826%2F46%29%5E7*12choose5 according to wolfram is .22267
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
can you do it using the a possion dist?
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
we have to decide what alpha is first
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
the average for the whole population is the same as the unknown small sample ie 12
 2 years ago

ujuge321Best ResponseYou've already chosen the best response.0
i know that part. but how should we figure out?
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
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
 2 years ago

ujuge321Best ResponseYou've already chosen the best response.0
how did you get 20/46?
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
pick a number between 0 and 5 ... there is 6 choices even though 50=5 so with 3.252.80=45cents there is 46 choices now less than $3 is 2.99 to 2.80 2.992.80=20 choices so prob(x<$3)=20/46
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
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
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
so we worked out alpha = 5.2173913 and x=5
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
sub into the possion equation and post your answer
 2 years ago

ujuge321Best ResponseYou've already chosen the best response.0
this question is tough.
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=5.2173913%5E5*exp%285.2173913%29%2F5%21 this gives the answer as 0.1746633
 2 years ago

beniceBest ResponseYou've already chosen the best response.2
which like we said earlier the possion dist is like bionomial.... in that its an estimate.. the possion dist works better for large numbers
 2 years ago
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