1 The following probability distribution represents the numb

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. SHOW YOUR WORK.

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?

Solution

Consider the table:

Thus,          
          
E(x) (mean) =    2.65   [ANSWER]

Var(x) = E(x^2) - E(x)^2 =    2.1075   [ANSWER, VARIANCE]  

s(x) =    1.451723114   [ANSWER, STANDARD DEVIATION]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!