71% of WhatApp users have given it a five-star rating on Google Play. Of the rem

Question

71% of WhatApp users have given it a five-star rating on Google Play. Of the remaining us- ers, 15%, 6%, 3%, and 5% have given ratings of four, three, two, and one stars, respectively to the application. a. Specify the probability distribution for the number of stars as rated by the users. b. Findthemeanofthisprobabilitydistribution.Interpret it c) Find the standard deviation of this probability distribution. Interpret it. d) Find P (X 2) where X =grade point score of a randomly selected student.

Explanation / Answer

Let, X =grade point score of a randomly selected student.

a) P(X = 1) = 0.05

P(X = 2) = 0.03

P(X = 3) = 0.06

P(X = 4) = 0.15

P(X = 5) = 0.71

b) Mean, E(X) = 1 * 0.05 + 2 * 0.03 + 3 * 0.06 + 4 * 0.15 + 5 * 0.71 = 4.44

c) E(X2) = 12 * 0.05 + 22 * 0.03 + 32 * 0.06 + 42 * 0.15 + 52 * 0.71 = 20.86

Var(X) = E(X2) - (E(X))2 = 20.86 - 4.442 = 1.1464

Standard deviation = sqrt(1.1464) = 1.0707

d) P(X > 2) = 1 - P(X = 1)

                  = 1 - 0.05

                  = 0.95

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