Unless announced otherwise, Exam 2 will be due on 10:05pm on Tuesday (March 6, 2018). The omission of the solution (both normal curve and area under z/t score and any other calculation) will result in zero. ate submission will be penalized 15 pts each day past the due date. Exam 2 submitted after the 10:15pm on due date will be penalized full credit. In order to receive a full credit, you MUST submit on the Blackboard: (i) answer for hand calculation named “YOUR LAST NAME_FIRST NAME_DATE_Exam2.pdf” or “YOUR LAST NAME_FIRST NAME_DATE_ Exam2.docx”

1. Probability

1-1. Assume that you have a distribution of prior arrests with a mean of 6 and a standard deviation of 2.5. (10pts)

a. What proportion of cases have between 2 and 6 arrests?

b. What proportion of cases have between 3 and 5 arrests?

1-2. Assume that in order to qualify for an internship that you are seeking, you must be in the top 10% of your class. The mean GPA in your class is 2.40 with a standard deviation of 1.2. What is the minimum GPA to qualify? (10 pts)

2. i) Draw a picture indicating ii) what proportion (area) of the normal curve lies

a. To the left of a z score of –1.92 (4pts)

b. To the right of a z score of 2.33 (4pts)

c. To the right of a z score of 1.45 or to the left of a z score of –1.45 (4pts)

d. In between a z score of –2.15 and .10 (4pts)

e. Is the left of a z score of –1.64 large? Explain (4pts)

3. Construct C.I. (25pts)

3-1. A researcher is interested in estimating the average starting salary among the population of municipal law enforcement officers in New Jersey. A random sample of 10 municipalities resulted in the following data:

Mean = $42,144

Standard deviation = $3,000

Construct and interpret a 95% confidence interval about the point estimate.

3-2. In a two-year survey of 100 census tracts in Seattle (WA), Rountree and Warner (1999) observed a mean official violent crime rate of 27.06 per 1,000, with a standard deviation of 33.81. Construct a 90% confidence interval around this mean. Now assume that Rountree and Warner had actually surveyed more census tracts in Seattle. How would their confidence interval be different?

3-3. Kreager (2007) in his study of violence and peer acceptance reported descriptive results for male and female students. The average age for 24,379 male students was 15.23 with a standard deviation of 1.65. Construct and interpret a 95% confidence interval for male age.

3-4. Kingsnorth et al. (2002) examined the case processing time (in days) from arraignment to disposition for cases processed by the Sacramento County District Attorney’s office. For the 58 cases that were rejected at intake, the mean processing time was 11.3 days with a standard deviation of 21.02.

Construct and interpret all three 90%, 95%, and 99% confidence interval.

3-5. Kingsnorth et al. (2002) examined the case processing time (in days) from arraignment to disposition for cases processed by the Sacramento County District Attorney’s office. For the 90 cases that resulted in a felony conviction, the mean processing time was 113.6 days with a standard deviation of 175.53. Construct 95% confidence intervals for each mean.

Construct and interpret all three 90%, 95%, and 99% confidence interval.