In order to estimate the total number of defective calculators out of the 15 000 produced, we first need to find the experimental probability that a randomly chosen calculator is defective.
Experimental Probability
We will use the inspector's results and compare the number of times the event we are interested in occurs to the number of times the experiment is done.
P = Times the event occurs/Times the experiment is done
In our case, the number of times that the experiment is done is the total number of calculators in the random sample the inspector selected, meaning that the experiment was conducted 450 times. The number of times that the events occurs is 4, as this is the number of defective calculators found in the sample. We have enough information to calculate the desired probability.
P(defective) = Times the event occurs/Times the experiment is done
The experimental probability that a randomly chosen calculator is defective is 2225.
Prediction
Now we are able to estimate the total number of defective calculators out of the 15 000 produced. To do so, let's denote the number of defective calculators as d and the total number of calculators produced as t. We will use the following formula.
d = P(defective) * t
We are considering a total of 15 000 calculators, so we will substitute 15 000 for t. The probability that a randomly chosen calculator is defective is 2225, as we found earlier. This means that we can substitute 2225 for P(defective).
