Again consider Exercise 4.32 (page 181) and the title-by-title analysis of the song We've Got It Goin'

Question:

Again consider Exercise 4.32 (page 181) and the title-by-title analysis of the song "We've Got It Goin' On" by the Backstreet Boys. Although not discussed in Exercise 4.32, Strategic Radio Research estimated the proportions of listeners familiar with the song who would give the song ratings of 5, 4, 3, 2, and 1 to be, respectively, .1978, .2967, .3077, .0879, and .1099. Assign the numerical values 1 through 5 to the ratings 1 through 5.
a. Find an estimate of the probability of this song's rating, x, by a randomly selected listener who is familiar with the song.
b. Find the popularity index for the song "We've Got It Goin' On" that would be reported by Strategic Radio Research. That is, find an estimate of the mean rating of this song that would be given by all listeners who are familiar with this song. Distribution
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