roblem 133 Expected value and standard deviation LO1 Sampson

roblem 13-3 Expected value and standard deviation [LO1]

Sampson Corp. is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given.

Possible
Market Reaction

Sales
in Units Probabilities
  Low response 30 .10
  Moderate response 50 .20
  High response 75 .40
  Very high response 90 .30

a.

What is the expected value of unit sales for the new product? (Do not round intermediate calculations and round your answer to the nearest whole unit.)

  Expected value units

b.

What is the standard deviation of unit sales? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Standard deviation units

Solution

in Units Probabilities px px^2
  Low response 30 .10 3 9
  Moderate response 50 .20 10 500
  High response 75 .40 30 2250
  Very high response 90 .30 27 2430

Total 245 1.00 70 5189

Expected value in units = 70

b) Variance = 5189-70^2 =289

STd dev = 17