A computer is programmed to take the sum of 400 draws made at random with replac

Question

A computer is programmed to take the sum of 400 draws made at random with
replacement from the magic box:

a. What is the value range for the sum of 400 draws (the possible lowest value and the largest value of the sum of 400 draws)?
b. What is the expected value and standard error of the sum of 400 draws?
c. What is the chance that the sum is less than 1500? (using the normal approximation)


please show how you get the answers

Explanation / Answer

a. Lowest possible value = 400*0 = 0 Highest Possible value = 400*8 = 3200 b. Let the total sum be X X = X1+X2+......+X400 => Expected Value of X = Exp(X1)+Exp(X2)+.....+Exp(400) Exp(X1) = Exp(X2) = ..... =Exp(400) = (0+2+4+6+8)/5 = 4 Therefore, Expected value of X = 4*400 = 1600 Variance of X = Var(X1) + Var (X2) + ...... + Var (X400) = 400 * Var (X1) => Standard Deviation of X = Sqrt(400)* Standard Deviation of X1 = 20 * Sqrt((42 + 22 + 02 + 22 + 42) / 5) = 56.5 Standard error = Standard deviation / vn = 56.5 /v400 = 2.83 C. Probability (Sum

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.