1. The following probability distribution represents the number of people living

Question

1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable.

    X      1         2        3          4        5         6        7

P(X)    .22      .35      .18        .13       .07      .03       .02

2. Use the binomial formula to compute the probability of a student getting 3 correct answers on a 7 question Quiz, if the probability of answering any one question correctly is 0.83.

3. Submit your answers to the following binomial questions. You may use the appendix tables 5 to answer parts a and b. According to a government study,15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 4 or more live in poverty?

b) what is the probability that 3 live in poverty?

c) what is the expected number (mean) that live in poverty?

(please answer the whole question)

Explanation / Answer

1) E(X)=sum(x*P(x))

V(X)=E(X^2)-(mean)^2

E(X^2)=sum(x^2*P(x))

sd(x)=sqrt(V(x))

E(X)=2.65

E(X^2)=9.13

V(X)=2.1075

sd(X)=sqrt(2.1075)=1.4517

2. n=7

x=3

p=0.83

P(x)=0.01671

Use BINOMDIST function in excel to find the above probability.

3. p=0.15

n=15

a) P(x>=4)=1-P(X<4)

P(X>=4)=1-0.987897=0.012103

b) x=3

P(x=3)=0.016662

c) E(X)=n*p=15*0.15=2.25

x P(x) x*P(x) x*x x*x*P(x) 1 0.22 0.22 1 0.22 2 0.35 0.7 4 1.4 3 0.18 0.54 9 1.62 4 0.13 0.52 16 2.08 5 0.07 0.35 25 1.75 6 0.03 0.18 36 1.08 7 0.02 0.14 49 0.98 2.65 9.13

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