Answer all 30 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted.
This exam has 300 total points.
Refer to the following table for Questions 1, 2, and 3. Show all work. Just the answer, without supporting work, will receive no credit.
The table shows temperatures on the first 12 days of October in a small town in Maryland.
Date 
Temperature 
Date 
Temperature 
Date 
Temperature 
Oct 1 
73 
Oct 5 
53 
Oct 9 
66 
Oct 2 
65 
Oct 6 
52 
Oct 10 
75 
Oct 3 
65 
Oct 7 
62 
Oct 11 
52 
Oct 4 
70 
Oct 8 
55 
Oct 12 
57 
1. 
Determine the fivenumber summary for this data. 
(10 pts)

2. 
Determine the mean temperature. 
(3 pts) 
3. 
Determine the mode(s), if any. 
(2 pts) 
 Obtain the fivenumber summary for the given data.
The ordered series needed to obtain the fivenumber summary is given below.
52 
52 
53 
55 
57 
62 
65 

65 
66 
70 
73 
75 
Minimum = 52
First Quartile = Mean of the 3^{rd} and the 4^{th} terms = (53 + 55)/2 = 54.5
Median = Mean of the two middle terms = (62 + 65)/2 = 127/2 = 63.5
Third quartile = Mean of the 9^{th} and the 10^{th} terms = (66 + 70)/2 = 68
Maximum = 75
 The mean temperature is,
.
 The mode(s) is (are) the highest frequent observation(s) in the given data. In the given data two observations 52 and 65 are repeated twice and the remaining are appeared only once.
Therefore, the required modes are 52 and 65.
Refer to the following frequency distribution for Questions 4, 5, 6, and 7. Show all work. Just the answer, without supporting work, will receive no credit.
The frequency distribution below shows the distribution for checkout time (in minutes) in
UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.
Checkout Time (in minutes) 
Frequency 
1.0  1.9 
6 
2.0  2.9 
7 
3.0  3.9 
2 
4.0  4.9 
3 
5.0  5.9 
2 
4. 
What percentage of the checkout times was less than 5 minutes? 
(5 pts) 
5. 
Calculate the mean of this frequency distribution. 
(5 pts) 
6. Calculate the standard deviation of this frequency distribution. (10 pts)
7. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)
 Obtain The percentage of the checkout times was less than 5 minutes,
 Obtain the mean of this frequency distribution:
Checkout Time (in minutes) 
Frequency, f 
Midvalue, x 
f*x 
1.0  1.9 
6 
1.45 
8.7 
2.0  2.9 
7 
2.45 
17.15 
3.0  3.9 
2 
3.45 
6.9 
4.0  4.9 
3 
4.45 
13.35 
5.0  5.9 
2 
5.45 
10.9 
Total 
20 
57 
 Obtain the standard deviation of this frequency distribution:
Checkout Time (in minutes) 
Frequency, f 
Midvalue, x 
f*x 
f*x^2 
1.0  1.9 
6 
1.45 
8.7 
12.615 
2.0  2.9 
7 
2.45 
17.15 
42.0175 
3.0  3.9 
2 
3.45 
6.9 
23.805 
4.0  4.9 
3 
4.45 
13.35 
59.4075 
5.0  5.9 
2 
5.45 
10.9 
59.405 
Total 
20 
57 
197.25 
 The mean decreases as the observation recorded incorrectly decreases the sum of the observations. The median remains the same as it is a measure of location not influenced much by the change in extreme observations.
Refer to the following information for Questions 8 and 9. Show all work. Just the answer, without supporting work, will receive no credit.
A 6faced die is rolled two times. Let A be the event that the outcome of the first roll is greater than 4. Let B be the event that the outcome of second roll is an odd number.
8. What is the probability that the outcome of the second roll is an odd number, given that the first roll is greater than 4? (10 pts)
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