Review – Probability and Statistics Name: ______
Directions: This is due the day of the quiz. Please complete and show work for all problems.
Example 1: Building a New High School
Yes / No / No answer / TotalMale / 119 / 116 / 6 / 241
Female / 154 / 114 / 6 / 274
Total / 273 / 230 / 12 / 515
The School Board of Waldo, a rural town in the Midwest, is considering building a new high school primarily funded by local taxes. They decided to interview eligible voters to determine if the school board should build a new high school facility to replace the current high school building. There is only one high school in the town. Every registered voter in Waldo was interviewed. In addition to asking about support for a new high school, data on gender and age group were also recorded. The data from these interviews are summarized below.
1. Find P(votes yes) / 2. Find P(votes no |male)3. Find P(male and votes yes) / 4. Find P(votes no | female)
5. Find P(votes yes or votes no answer) / 6. Find P(female | votes no)
Example 2
The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 miles.
7. Label the normal curve showing ±2 standard deviations from the mean. Include the percentages on the curve.
8. What is the range of mileages for 68% of the tires?
9. What percent of the tires last more than 59,400 miles?
10. What percent of tires last less than 34,800 miles?
11. What is the range of mileages for 95% of the tires?
12. Is it reasonable to expect the tires to last for 85,000 miles? Why or why not?
Example 3
16. What is the median of the data?
17. What is the range of the data?
18. For what % of the games did they score more than 67 points? How many games does that represent?
19. Which of the following can be seen on the box and whisker plot? Check all that apply.
□ The mean of the data.
□ The 75th percentile of the data
□ The range of the data
□ The median of the data.
□ The standard deviation of the data.
20. For this dataset, find the following features. Data: 41, 39, 28, 37, 42, 38, 40, 41, 37, 36, 42, 29, 36
Mean:
Median:
Mode:
Standard deviation:
21. Use the following histogram to answer the questions
a. Is the data set skewed or symmetric? If skewed, which direction? Explain.
b. Predict the mean and median for this data. Draw and label them on the histogram. Explain.
22. You roll a die 100 times. The results are shown in the table below.
a. Fill in the experimental probability for each outcome. (in fraction and percent forms)
Outcome / 1 / 2 / 3 / 4 / 5 / 6Number of Occurrences / 11 / 24 / 10 / 16 / 20 / 19
Probability
b. What is the theoretical probability of rolling a 2?
c. How could you better design an experiment so that your experimental probability for rolling a 2 in part “a” is closer to the theoretical probability in part “b”? Explain why.