1. The following data given the numbers of cars owned by randomly selected families.
| 1 |
1 |
2 |
3 |
2 |
4 |
1 |
3 |
2 |
1 |
| 3 |
0 |
2 |
1 |
2 |
3 |
2 |
3 |
2 |
2 |
| 1 |
2 |
1 |
1 |
1 |
3 |
1 |
1 |
1 |
2 |
| 2 |
4 |
2 |
3 |
1 |
3 |
1 |
2 |
2 |
4 |
Question :
a. Prepare a frequency distribution table for these data using single-valued classes.
b. Compute the relative frequency and percentage distributions.
c. Draw a bar graph for the frequency distribution.
d. What percentage of the families own two or more cars?
2. During a quality assurance check, the actual coffee content (in ounces) of six jars of instant coffee was recorded as 6.03, 5.59, 6.40, 6.00, 5.99, and 6.02.
a. Find the mean and the median of the coffee content.
b. The third value was incorrectly measured and is actually 6.04. Find the mean and median of the coffee content again.
c. Which measure of central tendency, the mean or the median, was affected more by the data entry error?
3. A consumer testing obtained the following milled per gallon in five test runs performed by three types of compact cars.
|
Run 1 |
Run 2 |
Run 3 |
Run 4 |
Run 5 |
| Car A: |
28 |
32 |
28 |
30 |
34 |
| Car B: |
31 |
29 |
31 |
29 |
31 |
| Car C: |
29 |
32 |
28 |
32 |
30 |
a. The manufacturer of Car A wants to advertise that car performed best in this test. Which measure of central tendency - mean, median or mode - should be used for their claim? Explain your reasoning.
b. The manufacturer of Car B wants to advertise that car performed best in this test. Which measure of central tendency - mean, median or mode - should be used for their claim? Explain your reasoning.
c. The manufacturer of Car C wants to advertise that car performed best in this test. Which measure of central tendency - mean, median or mode - should be used for their claim? Explain your reasoning.
4. Sample SAT scores for eight males and eight females are listed.
Male SAT scores: 1059 1328 1175 1123 923 1017 1214 1042
Female SAT scores: 1226 965 841 1053 1056 1393 1312 1222
a. Find the range, variance, and standard deviation of each data set.
b. Interpret the results in the context of the real-life setting.
5. The Wood County sheriff classifies crimes by age (in years) of the criminal and whether the crime as violent or nonviolent. As shown below, a total of 150 crimes were reported by the sheriff last year.
|
|
Age (in years) |
|
| Type of Crime |
Under 20 |
20 to 40 |
Over 40 |
Total |
| Violent |
27 |
41 |
14 |
82 |
| Nonviolent |
12 |
34 |
22 |
68 |
| Total |
39 |
75 |
36 |
150 |
a. What is the probability of selecting a case to analyze and finding it involved a violent crime?
b. What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old?
c. What is the probability of selecting a case that involved a violent crime or an offender less than 20 years old? Which rule of addition did you apply?
d. Given that a violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old?
e. Two crimes are selected for review by Judge Michelle. What is the probability that both are violent crimes?
6. Find the probability that when a couple has 3 children, they will have exactly 2 boys. Assume that boys and girls are equally likely and that the gender of any child is not influenced by the gender of any other child.