1. Describe the relationship between the mean and the median for the following distribution

2. Answer
The distribution is right skewed. This means that the mean gets pulled up towards the tail. Therefore, mean > median.

3. Scores on the SAT are normally distributed with a mean score of 1060 and a standard deviation of 50. Without using a calculator, estimate the percentage of students who have a score between 920 and 1050.

4. Answer Find the z-scores for 920 and 1050 first
Look up the z-scores in the table
Subtract the proportions
41.81%

5. Scores on the SAT are normally distributed with a mean score of 1060 and a standard deviation of 50. If the 530 juniors at PNHS took the SAT, how many would you expect to have a score above 1205?

6. Answer
Find the percentage of students who you would expect to score about
Take that percentage of 530
1 student

7. The average height (in inches) of a 16- year old is 58 inches with a standard deviation of 4 inches. Tammy is 5’9”. What is her z-score and what does it mean?

8. Answer
Her z-score is That means that her score is 2.75 standard deviations above 58 inches. She is taller than approximately 99.7% of 16 year olds.

9. Julie’s z-score on her recent reading test was -1
Julie’s z-score on her recent reading test was and the test scores of her class were normally distributed. What does this mean about Julie? What proportion of the class scored better than her?

10. Answer
Julie’s score is 1.47 standard deviations below the average. A proportion of about of the students did better than Julie.

11. Which is the least biased way to choose a sample of PNHS students?
Asking every 4th student who walks into the doors in the morning
Asking every student who has 5A study hall
ing a link to a survey to all of the students
Sending surveys to a randomly generated list
Asking every student whose ID number is between and

12. Answer D

13. A teacher is testing whether eating a mint during a test has an affect on a student’s test score. She wants to compare eating a mint to eating nothing, testing on both boys and girls. She plans on giving the boys the mints and giving the girls nothing. Why is this a poor experimental design?

14. Answer
Any observed difference could be due to the gender of the student or other factors, not the mint.

15. Kim uses a random number generator to choose 50 PNHS kids
Kim uses a random number generator to choose 50 PNHS kids. It just so happens that almost all of the students picked are Kim’s friends. Should she keep this sample? Why?

16. Answer
She should keep the sample because random selection is an impartial sampling method and if she removes participants she is introducing bias.

17. The mayor of Plainfield noticed that when ice cream sales are up, crime is up. He wants to close down all of the ice cream shops in Plainfield. Why is this a bad idea?

18. Answer
Just because ice cream sales and crime are correlated, does not imply causation. There could be another factor, such as weather, that is affecting crime.

19. The length and weight of a mouse is normally distributed
The length and weight of a mouse is normally distributed. The mean length is 3.4 inches with a standard deviation of 0.3 inches. The mean weight is 0.65 ounces with a standard deviation of 0.1 ounces. Mickey Mouse is 5.6 inches and weights 1 ounce. Which of his measurements is more extreme/unexpected?

20. Answer
Mickey Mouse’s z-score for his length is 7.33 and his z-score for his weight is His length is more extreme because it is over 7 standard deviations to the right of the mean.

21. Consider a city where it rains 25% of the time
Consider a city where it rains 25% of the time. Name 3 different ways you could perform a simulation to determine the number of times it rains in this city during 15 randomly chosen days.

22. Answer
Use a random number generator to choose 15 numbers between will represent rain and 2, 3, and 4 will represent no rain.
Use a deck of cards, and choose 15 cards with replacement. Spades will represent rain and clubs, hearts, and diamonds will represent no rain.
Use a random number generator to choose 15 numbers between will represent rain and will represent no rain.

23. A soccer coach wanted to know whether shooting a penalty kick with your dominant foot is better than your non-dominant foot. The coach had all of her players shoot 5 penalty kicks with their dominant foot and 5 penalty kicks with their non-dominant foot. She subtracted the number of shots made with the non-dominant foot from the dominant foot. The results are shown below. According to the simulation, what is the probability that a student missed all of the shots with their non-dominant foot and made every shot with their dominant foot? -3 4 3 2 -1 5 1 -2

24. Answer
1/13 so about 7.7%