The time to complete a standardized exam in the BYU-Idaho Testing Center is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68-95-99.7 rule, approximately what percentage of students will complete the exam in under fifty minutes? Give your answer accurate to one decimal place.

Given that X the time to complete a standardized exam in the BYU-Idaho Testing Center is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes.

We have 68 rule as 2/3 of total would lie within 1 std deviation, and 95 rule as nearly 95% lie within 2 std deviations from the mean.

We have std deviation = 10

Hence 2 std deviations from the mean

= Mean ±2 std deviations

=[tex]70[/tex]±20

= [tex](50,90)[/tex]

Below 50, 0.25 or 2.5% would complete the exam.

raphealnwobi raphealnwobi · Answer 2 · 2022-04-19T11:41:18+02:00

2.5% of students will complete the exam in under fifty minute

What is the empirical rule?

The empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation, 95% of the data falls within two standard deviation and 99.7% of the data falls within three standard deviation.

mean of 70 minutes and a standard deviation of 10. Hence:

95% is within = 70 ± 2(10) = (50, 90)

Percentage of students will complete the exam in under fifty minutes = (100 - 95%) / 2 = 2.5%

2.5% of students will complete the exam in under fifty minute

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