Question

3. How many silver cars is the dealer expected to sell, on average, out of five cars? Interpret this expected value in context.

Answer 1

Answer:

$E(X)= 0*0.27068 +1*0.40426+ 2*0.24151+3*0.07214+4*0.01077+5*0.00064=1.14998$

So then the expected number of silver cars to sell for this case in the next five car sales is approximately 1.15 for the 23% of the total manufacturing cars produced.

Step-by-step explanation:

Assuming this problem :"23% of the cars a certain automaker manufactures are silver. Below is the probability distribution for the number of  silver cars sold by a car dealer in the next five car sales."

The distirbution is given by:

Num. Silver cars     0      |          1   |     2     |       3    |       4     |       5     |

Probability        0.27068|0.40426|0.24151|0.07214|0.01077|0.00064|

And assuming the following questions

What is the probability of selling at most three silver cars? Interpret this probability in context

For this case we just need to find this:

$P(X\leq 3) = P(X=0) +P(X=1) +P(X=2)+P(X=3) = 0.27068+0.40426+0.24151+0.07214=0.98859$

So then the probability of selling at most 3 silver cars in the next five car salesfrom the 23% of the total manufactured cars is 0.98859.

What is the probability of selling between and including one and four silver cars? Interpret this probability in  context.

For this case we just need to find this:

$P(1 \leq X\leq 4) = P(X=1) +P(X=2) +P(X=3)+P(X=4) = 0.40426+0.24151+0.07214+0.01077=0.72868$

So then the probability of selling between 1 and 4 silver cars in the next five car sales from the 23% of the total manufactured cars is 0.72868  in the next five car sales.

How many silver cars is the dealer expected to sell, on average, out of five cars? Interpret this expected value in context

For this case we can find the expected value on this way:

$E(X)= 0*0.27068 +1*0.40426+ 2*0.24151+3*0.07214+4*0.01077+5*0.00064=1.14998$

So then the expected number of silver cars to sell for this case in the next five car sales is approximately 1.15 for the 23% of the total manufacturing cars produced.