Mathematics - Statistics homework 3

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1. A social psychologist interested in nonverbal communication decided to do an informal study on eye contact. Knowing that eye contact tends to be associated with emotional connection, she believed that most people would be uncomfortable maintaining eye contact for more than a few moments with a total stranger. To test this, she took a walk on a crowded street and counted how many seconds she could maintain eye contact with various strangers before they looked away. Her findings, in seconds, were:

3.20 3.15 1.80 1.11 2.70 2.25 2.15 1.72 1.65 4.71 3.20 1.78 2.50

Calculate the (a) range, (b) variance, and (c) standard deviation for these lengths of eye contact.

2. Senior sociology majors were given a comprehensive examination to assess how much they had learned in their sociology classes. The mean on the test was 74, and the standard deviation was 8. What percentage of the students had scores

a. Between 74 and 85?

b. Between 80 and 85?

c. Above 72?

d. Above 86?

e. Between 70 and 80?

f. Below 72?

g. Below 85?

3. Lilian (who is known for over exaggerating) has been bragging that she made a 100 on the comprehensive exam from question 2. Do you believe her? Justify your answer. (Hint: what are the chances of scoring a 100 or higher?)

4. A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating an undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40.

a. What is the percentile rank of a score of 172?

b. What is the Z score for a test score of 195?

c. What percentage of scores fall between 100 and 160?

d. What proportion of respondents should score above 190?