1) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a 15-munute period.
20, 31, 21, 28, 28, 33, 29, 27, 37, 25, 19, 18, 22, 34, 25, 11, 17, 41,32,30
2) Find the mode for the following data:
85,27,28,13,35,27,56,78,35,22,28,35,27
3) The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record, to the nearest one-tenth of a mile, the distance they travel one way from home to work. The six distances are 44, 58, 25, 49, 17, 19. Compute the variance to the nearest tenth.
4) A department store, on average, has daily sales of $49,776.44. The standard deviation of sales is $3,200. On Monday, the store sold $55,783.30 worth of goods. Find Monday’s z score. Was Monday an unusually good day?
5) Find the percentile score for the data point 210. The data set is 218, 220, 212, 206, 214, 226, 206, 204, 209, 208, 212, 222, 204, 207, 200, 201, 210, & 205. (nearest whole number)
6) Which score has the best relative position:
A) a score of 58.8 on a test for which the mean is 52 and standard deviation is 5
B) a score of 8.5 on a test for which the mean is 6.5 and standard deviation is 2.3
C) a score of 384.4 on a test for which the mean is 330 and standard deviation is 56.5
D) this cannot be determined unless we see all three tests.
7) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the mean waiting time. Round your answer to one decimal place.
Waiting time Number of
(minutes) customers
0-3 11
4-7 9
8-11 17
12-15 15
16-19 8
20-23 7
24-27 3
8) The test scores of 40 students are 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98
Find the 40th percentile score.
9) Find the odds against person A winning 2 of 3 games of chess from person B, if the probability of A winning any game is 2/7.
10) A IRS auditor randomly selects 5 tax returns from 76 returns of which 9 contain errors. What is the probability that she selects none of those containing errors? (3 decimal places)
11) A study conducted at a certain college shows that 44% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least three find a job in his or her chosen field within a year of graduating. (3 decimal places)
12) The following table contains data from a study of two airlines which fly to Las Vegas.
Number of flights Number of flights
which were on time which were late
Fox Airlines 67 11
Trop Airlines 55 9
If one of the 142 flights is randomly selected, find the probability that the flight selected is a Trop Airlines flight given that it was on time.
(4 decimal places)
13) The table below describes the smoking habits of a group of adults.
.
Nonsmoker Light smoker Heavy smoker Total
Male 444 57 21 522
Female 538 68 33 639
Total 982 125 54 1161
If four different people are randomly selected from the 1161 adults, find the probability that they are all nonsmokers. (3 decimal places)
14) 23% of all movies always have annoying , insensitive, people in the audience. What is the probability of going to 10 movies where less than 3 movies have these types in the audience. (3 decimal places)
15) A coin is tossed 22 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. The person predicts correctly on 15 tosses. What is the probability of being correct 15 or more times by guessing?. Does this probability seem to verify that the person has ESP? (3 decimal places)
16) The weights of certain machine components are normally distributed with a mean of 25.88 g and a standard deviation of 2.37 g. Find the two weights that separate the top 17% and the bottom 17%. These weights could serve as limits used to identify which components should be rejected. (2 decimal places)
17) Find the margin of error for the 98% confidence interval used to estimate the population proportion with n = 355 and x = 77.
(2 decimal places)
18) Find the minimum sample size you should use to assure that your estimate of the population proportion, p, will be within the margin of error of 0.05 at a 90% confidence level. The sample proportion is estimated by 0.38.
19) A group of 25 randomly selected students have a mean score of 70.2 with a standard deviation of 6.7 on a placement test. What is the 99% confidence interval for the mean score, m, of all students taking the test? (one decimal place)
20) Various temperature measurements are recorded at different times for a particular city. The mean of 22°C is obtained for 40 temperatures on 40 different days. Assuming that s = 7.5°C, test the claim that the population mean is 25°C. Use a 0.01 significance level.
21) A researcher wants to check the claim that convicted burglars spend an average of 13.7 months in jail. A random sample of 25 such cases are taken form court files and finds that the mean time spent in jail is 12.5 months with sd = 3.9 months. The researcher feels that the mean time is lower. Using the sample results, test the claim that the mean time should be lower at the .05 level of significance.
22) Given the linear correlation coefficient r and the sample size n, determine the critical value of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a
significance level of 0.05, r = 0.5641, n = 30.
23) Use the given data to find the equation of the regression line. Round the final values to 3 decimal places, if needed
x 2 4 5 8 15
y 2 7 6 11 12
24) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): Find the value of the linear correlation coefficient r.
(4 decimal places)
Temp 40 86 58 57 77 41 47 46 89
Growth 28 54 32 25 35 44 29 23 66
25) Based on the data from 16 students, the regression equation relating the number of hours of preparation (x) and test score (y) is y = 44.30 + 15.07x. The same data yield r = 0.514 and a mean value of y = 77.2. What is the best predicted test score for a student who spent 2 hours preparing for the test? (use the .05 significance level) (nearest whole number)