Question

question number 10. (10.00 points) a furniture store is having a sale on sofas and youre going to buy one. the advertisers know that buyers get to the store and that 1 out of 3 buyers change to a more expensive sofa than the one in the sale advertisement. let x be the cost of the sofa. what is the average cost of a sofa if the advertised sofa is $250 and the more expensive sofa is $375? 312.50 291.45 291.67 281.25 333.33 none of the above

Explanation:

Step1: Calculate the weighted - average

The probability that a buyer gets the advertised sofa is $p_1=\frac{2}{3}$, and its cost is $C_1 = 250$. The probability that a buyer gets the more expensive sofa is $p_2=\frac{1}{3}$, and its cost is $C_2 = 375$.
The formula for the expected value (average) of a discrete - random variable is $E(X)=p_1C_1 + p_2C_2$.

Step2: Substitute the values into the formula

$E(X)=\frac{2}{3}\times250+\frac{1}{3}\times375$.
First, calculate $\frac{2}{3}\times250=\frac{500}{3}\approx166.67$.
Second, calculate $\frac{1}{3}\times375 = 125$.
Then, $E(X)=\frac{500}{3}+125=\frac{500 + 375}{3}=\frac{875}{3}\approx291.67$.

Answer:

291.67