z-scores and Normal Distributions Homework
due Thursday 11/2/17
In addition to taking notes and being engaged with learning math during class time, you must complete the homework ON TIME in order to be eligible to retake the z-scores and Normal distributions exam. The exam will be on Friday 11/3/17.
1. Harold’s science class was launching pumpkins with catapults. The average distance achieved was 52 feet, with a standard deviation of 17 feet. Maude’s science class did the same activity, but they were launching apples. Her class average distance was 63 feet, with a standard deviation of 9 feet. The goal in each activity was to get the pumpkin to go as far as possible. Harold’s pumpkin travelled 41 feet. Maude’s apples travelled 51 feet.
a. Who did worse relative to their class? Who did better? Explain your answers with reference to the data.
b. Explain why you can’t calculate percentages in this problem.
2. What percentage of values are above one standard deviation below the mean in a Normal distribution?
3. What percentage of values are within two standard deviations of the mean in a Normal distribution?
4. What z-score corresponds to the bottom half of a Normal distribution?
5. What z-score corresponds to the top 30% of a Normal distribution?
6. What z-scores mark the middle 88% of a Normal distribution?
7. The weights of cats in a shelter is approximately normal with a mean of 11 pounds and a standard deviation of 2 pounds.
a. What percentage of cats weigh 8 pounds or less?
b. What percentage of cats weight between 7 and 9 pounds?
c. If a cat is heavier than just 10% of cats, how much does that cat weigh?