In STAT 200 last year, students were asked to rate how much they liked various k

Question

In STAT 200 last year, students were asked to rate how much they liked various kinds of music on a scale of 1 (don’t like at all) to 6 (like very much). Following is a probability distribution (with one probability not given) for females’ rating of Top 40 music.

X=Rating         1          2          3          4          5          6

Probability       .04        .05        .09       ??         .32       .26

Is X = music rating a discrete variable or a continuous variable? Explain.

What must be the value of the probability for X = 4 (the probability that rating equals 4)? Fill in the blank and Explain how you determined this.

Determine E(X), the mean rating given by females. Please show your calculation.

Find the probability that the rating given is 3 or less.

[5 pts] For each rating value, determine the cumulative probability.

X = Rating

1

2

3

4

5

6

Cumulative Probability

Use the cumulative probabilities just found as an aid in finding the probability that the rating of a randomly selected student would be greater than 4. Show work.

Suppose we are considering only the ratings of a randomly selected student would be greater than 4. Then, for those students, what is the probability that they exactly give the rating of 5.

X = Rating

1

2

3

4

5

6

Cumulative Probability

Explanation / Answer

Yes, X = music rating is a discrete variable. It can take discrete values like 0.04,0.05,…

In order to all the probabilities add up to 1, P(X=4)=1-(0.04+0.05+0.09+0.32+0.26)

=1-0.76=0.24

E(X)=1*0.04+2*0.05+3*0.09+4*0.24+5*0.32+6*0.26

=4.53

P(rating given is 3 or less)=0.04+0.05+0.09=0.18

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