Question

I need help with questions 2 and 3

Each outcome may be člassifled a ee success The binomial random variable is continuous. OI d) 2. A discrete random variable, X, has the following probability distribution: PCX .1 1 .2 2 4 3 .3 (a) What is the probability that X is not more than 1? (b) What is the probability that X is at least 2? (c) What is the mean of X? (d) What is the standard deviation of X? Electrospec makes very complex circuit boards and there is a 30 percent chance that an inspector will certify a defective board as being satisfactory. If you have 3 inspectors examine a particular defective board, what is the probability that all 3 inspectors will not catch the defect? (Hint: This can be solved as an independent probability or a binomial probability problem). 3. Research has revealed that forty percent of Internet company employees have stock options in their companies. Consider a random sample of 12 employees from an Internet company, (a) What is the probability that at least 7 employees have stock options in the company? (b) What is the mean number of Internet company employees who have stock options in their

Answer 1

Sch:2 has probability distribution A discrete random variable x x 10 1 2 3 0.2 0.4 0.31 SP(x)/ol Probability that X is not more than I = P(x41) = P(x=0) + P(x=1 = of+0.2 = 0.3 And 6 Probability that x is at least 2 = P(x>2) = P(x=2} + P(X=3) -0.4+0.3 = 0.7 And 6 Mean = E(X) = ² x PW) = oxp(o) + ixplu + 2x (2) + 3xp(3) -ot 1x0.2 + 2x0.4 +3x0.3 - 0.2 +0.8 +0.9 = 1.9 And & E(X²) = {x²p(a) = ² x plot 1² x P(1) + 2² x P (2) + 3² x P(3) -ot ixo.2 + 4x0.4 + 9x0.3 = 0.2 +1 6 +2.7 = 4.5 Var(x) = E(X) - Ex)] = 4.5 - (1.9) =0.89 Standard deviation of x = Var (x) = 10.89 = 0.9434 Ans.