Quiz: Probability Distributions &Binomial; Show all work for partial credit Name

Question

Quiz: Probability Distributions &Binomial; Show all work for partial credit Name: 1. Results from a "Best 5 out of 9" competition yield the distribution given below Find the mean and standard deviation for the probability distribution. X P(x) 5 0.09 6 0.18 7 0.27 8 0.34 9 0.12 2. a) At a local college, 40% of all students are full-time. If we randomly select 32 students what is the probability that exactly 10 are full-time? If we randomly select 32 students, what is the expected value and standard deviation for the number of full-time students? b)

Explanation / Answer

1) mean E(X) = 5 * 0.09 + 6 * 0.18 + 7 * 0.27 + 8 * 0.34 + 9 * 0.12 = 7.22

E(X^2) = 5^2 * 0.09 + 6^2 * 0.18 + 7^2 * 0.27 + 8^2 * 0.34 + 9^2 * 0.12 = 53.44

variance = E(X^2) - (E(X))^2

               = 53.44 - (7.22)^2 = 1.3116

Standard deviation = sqrt(1.3116) = 1.145

2)a) n= 32

p = 0.40

P(X = x) = nCx * p^x * (1 - p)^ (n - x)

P(X = 10) = 32C10 * (0.4)^10 * (0.6)^22 = 0.089

b) Expected value = n * p = 32 * 0.4 = 12.8

Standard deviation = sqrt(n * p * (1 - p) = sqrt(32 * 0.4 * 0.6) = 2.77

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