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ujuge321
 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?
ujuge321
 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?

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

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

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

ujuge321
 2 years ago
Best ResponseYou've already chosen the best response.0i did not get it. That is the answer.

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

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

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

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

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

ujuge321
 2 years ago
Best ResponseYou've already chosen the best response.0i know that part. but how should we figure out?

benice
 2 years ago
Best ResponseYou've already chosen the best response.2ahh 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

ujuge321
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get 20/46?

benice
 2 years ago
Best ResponseYou've already chosen the best response.2pick 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

benice
 2 years ago
Best ResponseYou've already chosen the best response.2what 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

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

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

ujuge321
 2 years ago
Best ResponseYou've already chosen the best response.0this question is tough.

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

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