candy, weights, distributions, yum

harbong · #1 $Old$ May 15th, 2008, 07:35 PM

so I have a stats problem that I can't figure out.

Assume that the distribution of mints produced with a label weight of 20.4 is N(21.34, .16)

15 mints are selected independently. let Y be the number of those that weight less than 20.857 g. determine P[Y≤2].

The chapter for this is only about three paragraphs long and doesn't touch on this type of problem...any help?
thanks in advance!

CaptainBlack · #2 $Old$ May 15th, 2008, 10:48 PM

Quote:

Originally Posted by harbong $View Post$

so I have a stats problem that I can't figure out.

Assume that the distribution of mints produced with a label weight of 20.4 is N(21.34, .16)

15 mints are selected independently. let Y be the number of those that weight less than 20.857 g. determine P[Y≤2].

The chapter for this is only about three paragraphs long and doesn't touch on this type of problem...any help?
thanks in advance!

Using the information that the weight of a mint is $\sim N(21.34, 0.16)$ calculate the probability $p$ that a single mints weight is less than $20.857$ .

In a batch of $15$ mints the number $y$ with weight less than $20.857$ has a binomial distribution $B(15, p)$ . This will allow you to calculate:

$P(Y \le 2)=b(0;15,p)+b(1;15,p)+b(2;15,p)$

RonL