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- From: Mathematics, Statistics and Probability
- Posted on: Wed 20 Jan, 2016
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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 49
Oct 3 65 Oct 7 62 Oct 11 52
Oct 4 70 Oct 8 55 Oct 12 57
1. Determine the five-number summary for this data. (10 pts)
2. Determine the mean temperature. (3 pts)
3. Determine the mode(s), if any. (2 pts)
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 at least 4 minutes? (5 pts)
5. Calculate the mean of this frequency distribution. (5 pts) TAT200 : Introduction to Statistics Final Examination, Spring 2014 OL2 Page 3 of 6
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)
Refer to the following information for Questions 8 and 9. Show all work. Just the answer, without supporting work, will receive no credit.
A 6-faced 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)
9. Are A and B independent? Why or why not?
A random sample of STAT200 weekly study times in hours is as follows:
4 14 15 17 20
10. Find the standard deviation. (10 pts)
11. Are any of these study times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.
There are 1500 juniors in a college. Among the 1500 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.
12. What is the probability that a randomly selected junior is in at least one of the two courses? (10 pts)
13. What is the probability that a randomly selected junior takes only one course?
A box contains 10 chips. The chips are numbered 1 through 10. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.
14. How many elements are in the sample space of this experiment? (5 pts)
15. What is the probability that the three numbers drawn are all multiples of 5? (10 pts) STAT200 : Introduction to Statistics Final Examination, Spring 2014 OL2 Page 4 of 6
Questions 16 and 17 involve the random variable x with probability distribution given below. Show all work. Just the answer, without supporting work, will receive no credit.
x 1 2 3 4 5
P x( ) 0.1 0.2 0.3 0.1 0.3
16. Determine the expected value of x. (10 pts)
17. Determine the standard deviation of x. (10 pts)
Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves. Let random number X be the number of serves Mimi returns. As we know, the distribution of X is a binomial probability distribution. If her opponent serves 10 times, please answer the following questions:
18. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (5 pts)
19. Find the probability that she returns at most 8 of the 10 serves from her opponent . (10 pts)
20. Find the mean and standard deviation for the probability distribution.
The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2
feet.
21. What is the probability that a randomly selected pecan is between 8 and 12 feet tall? (10 pts)
22. Find the 80th percentile of the pecan tree height distribution. (5 pts)
23. If a random sample of 64 pecan trees is selected, what is the standard deviation of the sample
mean? (5 pts)
24. A random sample of 625 SAT scores has a mean of 1500. Assume that SAT scores have a population standard deviation of 250. Construct a 95% confidence interval estimate of the mean SAT scores.
25. Given a sample size of 81, with sample mean 730 and sample standard deviation 90, we perform the following hypothesis test at the
0.05? ? level.
?0 H : 750
?1 H : 750
(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(b) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.
(c) What is your conclusion of the test? Please explain.
26. Consider the hypothesis test given by
: 530
: 530.
H
H
?
?
?
?
In a random sample of 225 subjects, the sample mean is found to be
525 . Also, the?x
25 .? ?population standard deviation is
(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(c) Is there sufficient evidence to justify the rejection of H0 at the 0.01 level?? ? Explain. (20 pts)
27. The UMUC Daily News reported that the color distribution for plain M&M’s was: 35% brown, 20% yellow, 20% orange, 15% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below.
Color Brown Yellow Orange Green Tan
Number 42 21 15 9 13
Assume we want to use a 0.10 significance level to test the claim that the published color distribution is correct.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer
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