Math 165

First Midterm

Dr. Wilson

1. A class took a test. The students' got the following scores.

94 85 74 85 77 100 85 95 98 95

Find the mean, median, mode, upper quartile, lower quartile, interquartile range, and standard deviation. Draw the stem and leaf plot, the box and whisker plot, the frequency distribution and the frequency histogram. Are there any outliers?

2. In a nationally administered standardized test, the mean was 1000 and the standard deviation was 75. You got a 1180 on the test. What percent of the people who took the test did worse than you?

3. Students in a class were given two quizzes. The scores are presented in the following table.

Student

Quiz 1

Quiz 2

A

5

9

B

4

7

C

2

5

D

6

10

E

3

4

a) Find the least squares regression equation which will be used to predict the scores on the second test as a function of the scores on the first test. i.e., let the scores on the first test be the explanatory variable and let the scores on the second test be the response variable.

b) Find the correlation coefficient r.

c) Use the regression equation to predict the score that student E should have gotten on the second quiz.

d) What is the residual for student E?

4. a) What is a probabilistic model?

b) How do you use a probabilistic model to compute the probabiltity of an event?

5. A pair of fair dice are rolled and the sum of the numbers on the top faces is noted.

6. A student took a multiple choice test and guessed on three questions. Each question had 5 possible answers. Let X denote the number of correct answers.

a) What are n and p for this problem?

b) Complete the following probability distribution.

x

P(x)

0

1

2

3

c) Draw the histogram

d) What is the probability of getting 2 or 3 correct answers by guessing?

7. In problem 6, suppose that another student decided to guess on all of the problems on the test. Suppose that there were 60 questions.

a) What would be the expected number of questions which would be correctly answered by guessing?

b) What is the standard deviation?

c) What is the probability that the student could get at least 20 correct by simply guessing on all of the quesions?

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