MS 150 Statistics q07 • Name:

In the world of marbles the larger shooter marbles are called taws and the smaller marbles that one tries to hit out of the circle are called ducks. The later term refers to the marbles being "sitting ducks" which do not move. Ducks do not all have the same mass in grams, each duck differs due to the manufacturing process. Twenty-six ducks were massed and found to have a mean mass of μ = 5.40 grams with a standard deviation of σ = 0.25 grams. Presume the distribution is normal for duck masses.

1. __________ What is the z-score for 5.40 gram duck?
2. __________ What is the z-score for 5.30 gram duck?
3. __________ What is the z-score for 5.00 gram duck?
4. p(x < 5.40) = __________ What percent of the ducks would be less than 5.40 grams?
5. p(x < 5.30) = __________ What percent of the ducks would be less than 5.30 grams?
6. p(x > 5.00) = __________ What percent of the ducks would be more than 5.00 grams?
7. p(5.00 < x < 5.30) = __________ What percent of the ducks would be between 5.00 grams and 5.30 grams?
8. p(x < __________ ) = 0.20 Below what mass are found the 20% least massive ducks?
9. p(x > __________ ) = 0.20 Above what mass are found the 20% most massive ducks??