27 The expected value and variance of a random variable x are as follows: E(x) 5

Question

27 The expected value and variance of a random variable x are as follows: E(x) 58.5 22.23 var X The random variable x is linearly transformed to y according to the following equation. y 10 4x The expected value of the transformed random variable y is 236 240 244 248 28 In the previous question, the variance of the transformed random variable is: 88.92 98.92 355.68 365.68 Tom is a salesman. He receives 20% ofthe price of the item sold as sales commission plus a fixed salary of $200 per week. Tom's average weekly sale is 25 items with a standard deviation of 8. The average price of items Tom sells is $250. Bob works 46 weeks a year. 29 Tom's average annual earnings is a $66,700 b $64,800 c $62,600 d $60,500 30 In the previous question, what is the standard deviation of the annual salary? a $20,360 b $18,400 c $16,600 d $14,750

Explanation / Answer

27)

E(X) = 58.5 ,

Var(X) = 22.23

y = 10 + 4x

E(Y) = 10 + 4 E(X)

= 10 + 4*58.5

= 244

28)

Var(y) = 42(var (x)) (variance of constant term is 0 ,that is var(10) = 0)

= 16 * 22.23

= 355.68

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