Answer to Question #346064 in Statistics and Probability for yoona

Question

according to its label, each coffee bag in a box contains 4g of coffee powder.in actual fact, the mass of coffee powder per bag has a mean 4.05g and a standard deviation of 0.05g. assuming that the mass of coffee powder in each bag is distributed normally, calculate the expected number of coffee bags which contain 3.95g to 4.10g of coffee powder in a box of 300 bags.

Answer 1

$$P(3.95<X<4.10)=P(Z<\dfrac{4.10-4.05}{0.05})$$

$$-P(Z\le\dfrac{3.95-4.05}{0.05})=P(Z<1)-P(Z\le-2)$$

$$\approx0.84134-0.02275=0.8186$$

$$0.8186(300)=246$$

The expected number of such coffee bags is 246.