Chapter 16, Problem 44E

(a)

To determine

To Explain: Random variables to use to convey the net income of the bicycle store.

Explanation of Solution

Given:

Deluxe Model mean = 3.2 bikes

Deluxe Model standard deviation = 0.8 bikes

Basic Model price (B) = $120

Basic Model standard deviation = 1.2 bikes

Fixed cost = $200

Deluxe Model price (D) = $150

Basic Model mean = 5.4 bikes

Calculation:

It will display net income as the amount of sales of the simple model motorcycles (B)and deluxe model bikes (D) minus the $200 fixing cost.

Net income

(b)

To determine

To find: the mean of the total income.

Answer to Problem 44E

$928

Explanation of Solution

Given:

Deluxe Model mean = 3.2 bikes

Deluxe Model standard deviation = 0.8 bikes

Basic Model price (B) = $120

Basic Model standard deviation = 1.2 bikes

Fixed cost = $200

Deluxe Model price (D) = $150

Basic Model mean = 5.4 bikes

Calculation:

The Net Income Equation of Part (a), and the B and D variable for the bikes defined for both models, must be used to measure the mean Net Income. The average simple model is 5.4 bikes with the average deluxe model 3.2.

  

Thus, the mean total income is $928.

(c)

To determine

To find: the standard deviation of the total income.

Answer to Problem 44E

$187.45

Explanation of Solution

Given:

Deluxe Model mean = 3.2 bikes

Deluxe Model standard deviation = 0.8 bikes

Basic Model price (B) = $120

Basic Model standard deviation = 1.2 bikes

Fixed cost = $200

Deluxe Model price (D) = $150

Basic Model mean = 5.4 bikes

Calculation:

The net income equation of part (a) without a fixed cost of $200 is needed to measure the standard variance of net income, since this is the constant variance and the squared price of the units is measured as standard deviation for the two. The standard model deviation is 1.2 motorbikes and 0.8 motorcycles.

  

  

Thus, the standard deviation of the total income is $187.45

(d)

To determine

To Explain: that need to create any assumptions in estimating the mean and about the standard deviation.

Explanation of Solution

In estimating the total net income, it had no calculations to make. However, it had to conclude that the sales of the two motorcycle models were separate, which implies that the selling for one model has little effect on the sell for the other model, when measuring the standard deviation of the net income.