Thread: Probability using the Normal Model

1. Probability using the Normal Model

This seems like it should be easy because I know the normal model is designated by (N) and I need to find the standard deviation (SD) but I do not think I have the correct formula. If someone could point me in the right direction I think (more like hope) I could get it on my own. Thank you.

The weight of potato chips in a medium-size bag is stated to be 10 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean 10.2 ounces and a standard deviation of 0.12 ounces. What is the probability that a randomly selected bag is underweight (less than 10 ounces)? Also, some chips are sold in "bargain packs" of 3 bags. What is the distribution of the mean of these three bags?

2. First question:

For any one bag, its weight X, has a distribution is given by $\displaystyle X \sim (10.2, 0.12^2)$

P(underweight) = $\displaystyle P (X < 10 ) = ?$

Second question:

$\displaystyle T = X_1 + X_2 + X_3$

where $\displaystyle X_i$ are individual bags.

Find E(T) and Var(T)

I've worked through them at the bottom if you're still stuck.

For the first one:

$\displaystyle P(Z< \frac{10 - 10.2}{0.12}) = P(Z < - \frac{5}{3} ) = 1 - P(Z< \frac{5}{3}) = ?$

Sorry, I don't have the tables on me. Can you check that?

For the second one:

$\displaystyle E(T) = E(X_1) + E(X_2) + E(X_3) = 10.2 + 10.2 + 10.2 = 30.6$

And $\displaystyle Var(T) = Var(X_1) + Var(X_2) + Var(X_3) = 0.12^2 + 0.12^2 + 0.12^2 = 0.0432$

So its distribution is given by $\displaystyle T \sim N (30.6, 0.0432)$