A salesperson has found that the probability of making various numbers of sales per day is presented in the following table. Calculate the expected number of sales per day and the standard deviation of the number of sales.

Question

Number of sales(Probability)
1(0.05) 2(0.16) 3(0.20) 4(0.25) 5(0.18) 6(0.10) 7(0.04) 8(0.02)

Answer 1

Find the mean first = sum of scores/number of scores

Sum of scores = (.05) + 2(.16)... + 8(.02) = ?

Number of scores = 1 + 2 + 3... + 8

Subtract each of the scores (.05, .16, .16, .2, .2, .2....) from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

I'll let you do the calculations.

Answer 2

μ = ∑[x * P (x)]
μ = [(0*0.06) + (1*0.25) + (2*0.37) + (3*0.25) + (4*0.06)]
μ = 0 + 0.25 + 0.74 + 0.75 + 0.24
μ = 1.98

σ2 = ∑[x2 * P(x)] – μ2
σ2 = [(02*0.06) + (12*0.25) + (22*0.37) + (32*0.25) + (42*0.06)] – 1.98
σ2 = [(0*0.06)+(1*0.25)+ (4*0.37) + (9*0.25) + (16*0.06)] – 3.92
σ2 = [0 + 0.25 + 1.48 + 2.25 + 0.96] – 3.92
σ2 = 4.94 - 3.92
σ2 = 1.02

σ = √σ2
σ = √1.02
σ = 1.009