# Sample Distribution Probability (unsure if correct answer)

#### vil33

##### New Member
1.
Carlinville, Illinois, has just started an ambitious recycling program. Special
trucks collect recyclable products once a week, sorted into barrels of paper, glass, and plastic.
The amount of glass recycled per week by a single household is normally distributed with
mean 27 pounds and standard deviation 7 pounds. Suppose 12 households are randomly
selected.
a. What is the probability that the total glass collected for the 12 homes will be less than
350 pounds?
b. If the total glass collected for the 12 homes is more than 400 pounds, the recycling
plant will make a profit. Find a value of population mean such that the probability of
making a profit is 0.10.

1a.

mean = 27 * 12 = 324 deviation = root of (7^2) * 12 = 24.25

P(X < 350) = P(X-324/24.25 < 350-324/24.25)

P(X < 350) = P(Z < 1.07)

P(Z < 1.07) = 0.8577

1b.

-1.28 = 400 - x/24.25
x = 368.96

I'm not sure if I used the correct methods to find the mean and std deviation or if I used them correctly in the formula and whether my answers are correct.
Thanks.