Suppose we would like to know the opinion of our students with respect to a tuition increase proposed

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

DIRECTIONS:

• Read all questions carefully.

• You must show all work and provide rationales.

• You must show all calculator commands relevant and used to help you arrive at the solution to each problem.

• The rounding convention for all probability problems is to four decimal places. All other problems should be rounded to two places.

• You must show all work and answers on this exam file.

• This section is worth 90 points.

PLEDGE:

By signing below, I attest the following is true: on my honor, I have neither received nor given help on any of the material included in this exam.

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Problem 1

(24 pts Total) Suppose your professor opens a large enough size bag of candy for family enjoyment. If there are 58 pieces of candy in the bag and he picks four at random to eat, calculate the probability of the following events( There are originally 17 red pieces, 11 green pieces, 12 yellow pieces, and the remaining pieces are orange.):

A) One Yellow Piece

B) At least One Orange Piece

C) No Green Pieces

D) Five Red Pieces

Problem 2

(21 pts Total) Suppose we have the following list of professional football teams:

(10 pts) Please select a random sample of size 16 representing both conferences combined. You must show the calculator commands and inputs that helped you make sample. You must also, list the sample in terms of the teams.

(11 pts) Please select a cluster sample of size 16 from the list of teams. You must show the calculator commands and inputs that helped you make sample. You must also, list the sample in terms of the teams. 

Problem 3

(22 pts Total) Suppose I found out that through genetic testing that the probability of me having a son is 0.657. I would like to ensure I have a son, while having no more than 3 children.

(10 pts) Create a probability model for estimating the number of children that would ensure having one son.

(6 pts) What is the expected value (i.e. average) number of children that would ensure a son?

(6 pts) Calculate the standard deviation of the number of children for the above context.

Problem 4

(33 pts) Suppose we would like to know the opinion of our students with respect to a tuition increase proposed. We took 54 random students from the population of Santa Fe College and asked their opinion. It was revealed that 31 percent of our respondents favor the tuition hike.

(21 pts) What distribution/model would we use to model the number of negative views in the fifty-four students picked? (Hint: Please check all conditions of any model you claim.)

Use the model you claimed in part A to calculate the following, assuming each respondent is picked at random:

Note: You must show all calculator commands, inputs, and output. Explain your process as you are teaching me.

(6 pts) P(exactly 12 people who would oppose tuition hike)

(6pts) P(at least 25 people who oppose tuition hike)

Attachments:

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