Question

after trying out a new fertilizer, a farmer counted the number of blueberries on each of her bushes. blueberries per bush 132 132 132 208 208 208 694 694 694 694. x is the number of blueberries that a randomly chosen bush has. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate the total number of bushes

There are 3 bushes with 132 blue - berries, 3 bushes with 208 blue - berries and 4 bushes with 694 blue - berries. So the total number of bushes is $3 + 3+4=10$.

Step2: Calculate the sum of blue - berries

The sum of blue - berries is $3\times132 + 3\times208+4\times694=396 + 624+2776 = 3796$.

Step3: Calculate the expected value

The expected value $E(X)$ of a discrete random variable is the sum of all possible values of the variable multiplied by their respective probabilities. Here, since we are using the frequency approach, the expected value is the total number of blue - berries divided by the total number of bushes. So $E(X)=\frac{3796}{10}=379.6$.

Answer:

379.6