Question

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?

Answer 1

Is this a poisson distribution?

Answer 2

yep

Answer 3

i'm not sure on this.

@callisto

Answer 4

ok

Answer 5

if it uniform all prices are equally likely.

so the prob of one store charging less than 3.00
is 20 out 46

Answer 6

no it is 0.22

Answer 7

how did you get that?

Answer 8

i did not get it. That is the answer.

Answer 9

so now it a bionomial which is very similar to the poission dist.

12C5*(20/46)^5*(26/46)^7

Answer 10

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

according to wolfram is .22267

Answer 11

okay. Thanks.

Answer 12

can you do it using the a possion dist?

Answer 13

how??

Answer 14

we have to decide what alpha is first

Answer 15

hmm... i see.

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

how did you get 20/46?

Answer 20

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

Answer 21

ok.

Answer 22

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

Answer 23

so we worked out alpha = 5.2173913
and x=5

Answer 24

sub into the possion equation
and post your answer

Answer 25

0.6160?

Answer 26

this question is tough.

Answer 27

http://www.wolframalpha.com/input/?i=5.2173913%5E5*exp%28-5.2173913%29%2F5%21

this gives the answer as 0.1746633

Answer 28

which like we said earlier the possion dist is like bionomial....

in that its an estimate..

the possion dist works better for large numbers

Answer 29

goodnight

Answer 30

ok. good night