1. Make a box-and-whisker plot of the data. Find the interquartile range.
2. The number of calls received by a crisis hotline during 18 randomly selected days is listed. Identify the outlier, and describe how it affects the mean and the standard deviation.
| 50 | 57 | 77 | 66 | 53 | 72 |
| 51 | 88 | 82 | 70 | 62 | 64 |
| 69 | 88 | 98 | 65 | 14 | 68 |
3. An experiment consists of rolling a number cube. What is the probability of rolling a number greater than 4? Express your answer as a fraction in simplest form.
Make a box-and-whisker plot of the data.
4. average daily temperatures in Tucson, Arizona, in December:
56, 65, 54, 50, 54, 61, 52, 58, 63, 63, 58, 57, 51, 61, 64, 58, 62, 64, 58, 63
5. The table shows the results of a survey of college students. Find the probability that a student is taking a humanities class, given the student is male. Round to the nearest thousandth.
First Class of the Day for College Students
| Male | Female | |
| Humanities | 100 | 70 |
| Science | 80 | 100 |
| Other | 55 | 65 |
Find the mean, median, and mode of the data set. Round to the nearest tenth.
6. test scores on a math exam:
67, 96, 69, 75, 98, 75, 84, 96, 81, 84, 84, 83, 86, 76, 83, 69, 88, 73, 98, 81, 74, 74
7. Susan keeps track of the number of tickets sold for each play presented at The Community Theater. Within how many standard deviations of the mean do all the values fall?
154, 167, 142, 131, 71, 87, 151, 109, 131, 69, 154, 120
8. In a sample of 120 teenagers, 22 have never been to a live concert. Find the sample proportion for those who have never been to a live concert.
Find the mean and standard deviation of the of data. Round to the nearest tenth.
9. 38, 68, 55, 53, 66, 51, 44, 68
Find the outlier in the set of data.
10. 22, 17, 10, 35, 24, 18, 23, 14
11. The scores on an exam are normally distributed, with a mean of 85 and a standard deviation of 7. What percent of the scores are less than 92?
12. A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a crop of onions with diameters that are normally distributed, with a mean diameter of 2.75 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?
13. A bag contains hair ribbons for a spirit rally. The bag contains 2 black ribbons and 10 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that Lila selects a black ribbon and Jessica selects a green ribbon? Express your answer as a fraction in simplest form.
14. The table shows the distribution of the labor force in the United States in the year 2000. Suppose that a worker is selected at random. Find the probability that a female works in the Industry field. Express your answer as a decimal, and round to the nearest thousandth.
| Agriculture | Industry | Services | |
| Male | 3,132,000 | 25,056,000 | 50,112,000 |
| Female | 667,000 | 8,004,000 | 57,362,000 |
15. The numbers of cookies in a shipment of bags are normally distributed, with a mean of 55 and a standard deviation of 2. What percent of bags of cookies will contain between 53 and 57 cookies?
Find the values of the 30th and 90th percentiles of the data.
16. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20
17. A set of data with a mean of 56 and a standard deviation of 5.8 is normally distributed. Find the values that are 1 standard deviation from the mean.
18. The circle graph shows the probability distribution for how often people went to the grocery store last week.
a. Draw a bar graph of the distribution.
b. Find P(visited the grocery store at least once).
Find the range and interquartile range of the data. Round to the nearest tenth.
19. 9, 21, 50, 9, 26, 26, 13, 33, 9, 18
Test MIDTERM STATS CAU (Show Work) Spring 2020
Answer Section
SHORT ANSWER
1.
Interquartile range: 5.5
2. The outlier is 14. The outlier in the data set causes the mean to increase from about 66.3 to about 69.4 and the standard deviation to decrease from about 18.6 to about 13.7.
3.
4.
5. 0.426
6. mean = 81.5, median = 82, mode = 84
7. 2
8. 18%
9. mean = 55.4;
standard deviation = 10.5
10. 35
11. 84%
12. 16%
13.
14. 0.121
15. 68%
16. 30th percentile = 9;
90th percentile = 20
17. 50.2 and 61.8
18. a.
b. 92%
19. range = 41; interquartile range = 17
