THE STUDENTS IN MR HENLYS CLASS PREDICTED THAT IF THEY EACH ROLLED A DIE 90 TIMES THE RESULT OF 1 OUT OF EVERY 6 ROLLS WOULD BE A 5. Each student then completed the experiment which result best supports the prediction of getting a 5 once out of 6 times. ( the question didn't say how many students were in the class)

Question

THE STUDENTS IN MR HENLYS CLASS PREDICTED THAT IF THEY EACH ROLLED A DIE 90 TIMES THE RESULT OF 1 OUT OF EVERY 6 ROLLS WOULD BE A 5. Each student then completed the experiment which result best supports the prediction of getting a 5 once out of 6 times. ( the question didn't say how many students were in the class)

You need to finish the problem.

Answer 1

To solve this problem, we need to compare the experimental result of rolling a die 90 times with the predicted probability of getting a 5 once out of every 6 rolls.

The predicted probability of getting a 5 once out of every 6 rolls is 1/6. This means that out of every 6 rolls, we would expect one of them to be a 5.

Let's assume there were "n" students in Mr. Henly's class who performed the experiment by rolling a die 90 times each. In each student's experiment, we would expect approximately (1/6) * 90 = 15 rolls to be a 5 if the prediction is correct.

Now, we need to check if any student's experimental result is close to the expected value of 15. We can calculate the margin of error to determine if a result deviates too far from the prediction.

To calculate the margin of error, we can use the concept of confidence intervals. One common method is to use a 95% confidence interval, which means we want to be 95% confident that the true proportion of rolls that result in a 5 falls within a certain range.

Using this approach, we can calculate the margin of error using the formula:
Margin of Error = 1.96 * √[(1/6) * (5/6) / 90]

Here, 1.96 is the z-value for a 95% confidence interval, and √[(1/6) * (5/6) / 90] represents the standard error.

Next, we can calculate the upper and lower bounds of the confidence interval by adding and subtracting the margin of error from the expected value of 15.

Upper Bound = 15 + Margin of Error
Lower Bound = 15 - Margin of Error

If any student's experimental result falls within this range, it would provide support for the prediction that one out of every six rolls would be a 5.

Please note that the number of students in the class is not mentioned in the question. If it is provided, you would need to calculate the experimental result for each student separately.