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. Show Your Calculations for the Mean.X 1 2 3 4 5P(X) .32 .39 .17 .08 .042. Use the binomial formula to compute the probability of a student getting 7 correct answers on a 10 question Quiz, if the probability of answering any one question correctly is 0.73. SHOW YOUR WORK.3. Submit your answers to the following binomial questions. You may use the appendix table B #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 20 children is selected:a) what is the probability that 5 or more live in poverty?b) what is the probability that 4 live in poverty?c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?

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