# Thread: candy, weights, distributions, yum

1. ## candy, weights, distributions, yum

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?

2. Originally Posted by harbong
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?
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:
$P(Y \le 2)=b(0;15,p)+b(1;15,p)+b(2;15,p)$