Question

can someone please help me with these questions at least by 11:00 PM tonight because I tried but was wrong. thank in advance

3. Question Details TEAFMAC2 2.4.026 My Notes Lou Gehrig has a lifetime batting average of 0.34. Assume that Lou Gehrig came to bat officially four times every game played. What would be Lou Gehrig's probability getting at least two hits in a game? (Round your answer to six decimal places.) 0.038594X

Answer 1

Sample size = n = 4 success probability = p given np = 0.34 p = .34/4 = 0.085 q = 1 - p = 0.915 Using Binomial distribution P(X = r)^nC_r p^r q^n - r =^4C_r (0.085)^r (0.915)^4 - r p(atleast 2) = P(X greaterthanorequalto 20 = P(X = 2) + P(X = 3) + P(X = 4) =^4c_2 (0.085)^2 (0.915)^2 +^4c_3 (0.085)^3 (0.915)^1 +^4c_4 (0.085)^4 (0.915)^0 = 0.038593 = 0.038594 Its correct Mean mu = sigma x_i P(x_i) = -6(0.12) - 5(.16) - 4(0.44) - 3(0.13) - 2(0.15) = -3.97 variance sigma^2 = sigma x_i^2 P(x_i) - mu^2 = 36 (0.12) + 15 (0.16) + 16(0.44) + i(.13) + 4(0.15) - (-3.97)^2 = 1.3691 Standard deviation sigma = 1.1700