Regina has a bag of 6 orange marbles and 6 black marbles. She picks a marble at random and then puts it back in the bag. She does this 24 times. The results are shown in the table. Determine the percent error of pulling a black marble in Regina’s experiment. Show your work and round your answer to the nearest hundredth.
To determine the percent error of pulling a black marble in Regina's experiment, we can compare the observed frequency (the number of times a black marble was pulled) with the expected frequency (the number of times we would expect to pull a black marble if the marbles were selected randomly).
In this case, Regina conducted the experiment 24 times, so the total number of marble picks is 24.
Since the bag contains 6 black marbles and 6 orange marbles, the probability of pulling a black marble on any given trial is 6/12 or 1/2.
So the expected frequency of pulling a black marble in 24 trials can be calculated as (1/2) * 24 = 12.
Let's see the table of observed results:
| Observed Frequency |
|----------------------|
| 9 |
To calculate the percent error, we need to find the absolute difference between the observed and expected frequencies, divide it by the expected frequency, and then multiply by 100:
Percent Error = (|Observed Frequency - Expected Frequency| / Expected Frequency) * 100
In this case, the observed frequency is 9, and the expected frequency is 12.
Using the formula:
Percent Error = (|9 - 12| / 12) * 100
Calculating the absolute difference:
Percent Error = (3 / 12) * 100
Simplifying the fraction:
Percent Error = (1 / 4) * 100
Calculating the decimal value:
Percent Error = 0.25 * 100
Finally, calculating the percent value:
Percent Error = 25.00%
Therefore, the percent error of pulling a black marble in Regina's experiment is 25.00%, rounded to the nearest hundredth.