Question

Ray Liu is a sales rep in northern California for high-end golf equipment. Each day, he makes 10 sales calls (n = 10). The chance of making a sale on each call is thought to be 25% (p = 0.25).

Assume this problem is appropriate for the binomial probability distribution.

A. E(x) =
Enter your answer rounded to 1 decimal in the format 1.2, with no other text or symbols.

B. σ_x =
Enter your answer rounded to 1 decimal in the format 1.2, with no other text or symbols.

C. Compute the following probabilities for Ray's calls tomorrow. Enter your responses in decimal format rounded to 3 decimals, in the format 0.123 with no other text or symbols.

The probability of making exactly 3 sales =

The probability of making fewer than 4 sales =

The probability of making more than 5 sales =

Answer 1

A) E(X) = n * p = 10 * 0.25 = 2.5

B) = sqrt(np(1 - p))

          = sqrt(10 * 0.25 * 0.75) = 1.4

c) P(X = x) = nCx * p^x * (1 - p)^{n - x}

i) P(X = 3) = 10C3 * (0.25)^3 * (0.75)^7 = 0.250

ii) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 10C0 * (0.25)^0 * (0.75)^10 + 10C1 * (0.25)^1 * (0.75)^9 + 10C2 * (0.25)^2 * (0.75)^8 + 10C3 * (0.25)^3 * (0.75)^7 = 0.776

iii) P(X > 5) = 1 - P(X < 5)

                   = 1 - P(P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))

                   = 1 - (10C0 * (0.25)^0 * (0.75)^10 + 10C1 * (0.25)^1 * (0.75)^9 + 10C2 * (0.25)^2 * (0.75)^8 + 10C3 * (0.25)^3 * (0.75)^7 + 10C4 * (0.25)^4 * (0.75)^6 + 10C5 * (0.25)^5 * (0.75)^5)

                   = 1 - 0.980 = 0.020