Answer to Question #278683 in Statistics and Probability for Ivan

Question

Cereal boxes are filled at a factory. Through extensive sampling, it is found that their equipment fills the boxes to a mean of 502 grams, with a standard deviation of 3.1 grams.

10,000 boxes of cereal are produced each day. 

In a daily run, how many cereal boxes are expected to weigh between 500 and 504 grams?

Answer 1

Solution:

$\mu=502,\sigma=3.1 \\ X\sim N(\mu,\sigma) \\ P(500<X<504)=P(X<504)-P(X<500) \\=P(z<\dfrac{504-502}{3.1})-P(z<\dfrac{500-502}{3.1})$

$=P(z<\dfrac{2}{3.1})-P(z<\dfrac{-2}{3.1}) \\=P(z<0.65)-P(z<-0.65) \\=2P(z<0.65)-1 \\=2(0.74215)-1 \\=0.4843$

So, required no. of cereal boxes $=10000\times0.4843=4843$