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.

2 answers

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 ID
   528525

   Created
   April 10, 2011 4:15pm UTC

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   https://questions.llc/answers/528525

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

   Answer ID
   2346080

   Created
   March 22, 2022 10:14am UTC

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   https://questions.llc/answers/2346080