Math 116 01&02: Test #3 (Chapters 11 15) Name

Math 116 – 01&02: Test #3 (Chapters 11 – 15) Name:

Show work when appropriate to get full credit for correct answers.

Give grammatically correct explanations when asked to explain or support an answer.

1. A statistics teacher wants to know how students feel about the introductory statistics course taught at her college. She decides to administer a survey to a random sample of students taking the course. She has several sampling plans that she considers. Name the sampling strategy in each. (5 points each)

(a) She randomly selects 15 students from each class rank (freshman, sophomore, junior and senior).

(b) She randomly chooses 60 students from all that are taking the course.

(d) She randomly selects a class rank (freshman, sophomore, junior, or senior) and then surveys every student of that rank.

2. The owner of a shopping mall wishes to expand the food court. He wants to find out what types of food the shoppers in this mall would like to see added. He is in the mall every morning, so he randomly selects 500 customers during weekday mornings to determine this. What type of bias is definitely present in this scenario? Explain. (10 points)

3. In a bag are 24 ping-pong balls. Eight of them are red, eight of them are white, and eight of them or blue. The balls are numbered 1 through 8 for each color.

(a) One ball is randomly selected from the bag. Find the following. (5 points each)

(i) P(ball has a 5 on it)

(ii) P(ball is white and has an odd number on it)

(iii) P(ball is red or has an even number on it)

(b) Three balls are selected (one at a time with replacement). Find: (5 points each)

(i) P(all three balls are blue)

(ii) P(exactly two of the balls are red)

(iii) P(at least one of the balls is white)

(i) P(all three balls are blue)

(ii) P(no 4 or 5 is chosen)

4. A survey of local car dealers revealed that 64% of all cars sold last had a CD player, 28% had alarm systems, and 22% had both. Define D = “had a CD player” and A = “had an alarm system”. Find each of the following probabilities and explain what each means in context. A Venn diagram may be helpful. (5 points each)

(a)

(b)

(c)

(d)

Space to draw a Venn diagram if you’d like…

5. At a certain university, of the students who choose to live on campus, 10% are seniors, 20% are juniors, and the rest are underclassman. The most desirable dorm is the newly constructed Gold dorm, and 60% of the seniors elect to live there, 15% of the juniors also live there, while only 5% of the underclassmen live there. A single student living on campus at this university is chosen at random. Find the following. (5 points each)

Hint: A tree diagram may be helpful.

(a) P(student lives in the Gold dorm)

(b) P(student is an underclassman and not living in the Gold dorm)

(d) P(student does not live in the Gold dorm given that the student is a junior)

6. The table below shows the results of survey investigating which high school science class students preferred and which foreign language they were taking. One student from this study is selected at random. Find the following: (5 points each)

Chemistry / Physics / Biology / TOTAL
French / 16 / 10 / 8 / 34
Spanish / 35 / 23 / 44 / 102
TOTAL / 51 / 33 / 52 / 136

(a) P(student prefers Physics)

(b) P(student is taking Spanish and prefers Chemistry)