Question

A survey conducted by a song rating service finds that the percentages of listeners familiar with poker face by lady gaga who would give the song ratings of 5, 4, 3, 2, and 1 are, respectively, 50 percent, 18 percent, 19 percent, 8 percent, and 5 percent. assign the numerical values 1, 2, 3, 4, and 5 to the (qualitative) ratings 1, 2, 3, 4, and 5 and find an estimate of the probability distribution of x = this song’s rating by a randomly selected listener who is familiar with the song.

Answer 1

The probability distribution is shown in the table below

The value of the expected mean, E(X), is given by

E(X) = 5(0.5) + 4(0.18) + 3(0.19) + 2(0.08) + 1(0.05) = 4

Which represents the estimated rating of the song