Practice Exam #1

You are a full time college professor of statistics. Over your ten-year teaching statistics, you collected enough empirical evidence to estimate that, in average 20% of your students earn an A at the end of the course, 40% earn a B, 20% earn a C, and 10% earn a D. You are currently teaching a class of 108 students and you expect all the students in your classroom to complete the semester and earn a grade at the end.

1.       What is the expected number of students in your class who will earn an A or B (Do no round)?

Answer: 64.8

2.       If 4 points are awarded for an A, 3 for a B, 2 for a C, and 1 point for a D, what is the expected class GPA? Do not round answer.

Answer: 2.5

3.       Let’s suppose you randomly group the 108 students into 12 teams of 9 students each, so that 12x9= 108. What is the expected number of As in a given team? Do not Round

Answer: 1.8

4.       What is the probability that a given team of nine students does not contain any F Students? (3 decimals)

Answer: 0.387

5.       What is the probability that a given team of nine students contains at least one F Student? (3 decimals)

Answer: 0.613

6.       How many of the 12 teams do you expect not to include any F Students ( 1 Decimal)

Answer: 4.65

7.       As you look back to the statistics of your 10-year teaching experience, you notice that 40% of your students have been women, 20% of your students have earned an A, and 12% of your students have been men AND earned an A.

Calculate the probability of having a student who has not earned an A

Answer: 0.80

8.       Calculate the probability of having a student who is a woman and earned an A

Answer: 0.08

9.       Calculate the probability of having a student who is a woman or earned an A

Answer: 0.52

10.   Calculate the probability of having a student who earned an A, given the fact she is a woman

Answer: 0.2

11.   Calculate the probability that a student is a man, given the fact he earned an A

Answer: 0.6

12.   For a student, being a man and earning an A are disjoint events

Answer: False

13.   For a student, being a man and earning an A are independent events

Answer: True

14.   Comment on the shape of the distribution. Be Specific

Answer: Unimodal and skewed to the left (no need to answer)

15.   Why would you expect the mean exam score for the class of staistics students to be lower than the medians?

Answer: because the distrubtion is skewed to the left (no need to answer)

16.   For this data set, the median is a more appropritate measure of central tendency than the mean.

Answer: True (no need to answer)

17.   Are there any outliers?

<60: 1 Student

61-68: 2 Students

69-76: 4 Students

77-84: 5 Students

85-92: 8 Students

93-100: 6 Students

>100: 1 Student

Answer: All data points are within the fences. There are no outliers

18.   What is the z-score for a student with exam score of 90? (use 2 decimal points)

Answer: 0.52

19.   Suppose now that a student who complained about a wrongly graded exam had her score updated from a 90 to 100. Indicate whether each of the following summary statistics will increase, decrease, or stay the same.

Mean: Increases

Median: Stays about the same

Range: Stays about the same

IQR: Increases

 

St. Dev: Increases

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