Question

the testing times for a group of college students were normally distributed with a mean of μ = 30 minutes and a standard deviation of σ = 2.5 minutes. the bell curve below represents the distribution for testing times. the scale on the horizontal axis is equal to the standard deviation. fill in the indicated boxes. used the empirical rule to complete the following statements: 68% of testing times were between minutes and minutes. 95% of testing times were between minutes and minutes. 99.7% of testing times were between minutes and minutes. 50% of testing times were below minutes. question help: video message instructor post to forum

Explanation:

Step1: Recall the Empirical Rule for normal - distribution

The Empirical Rule states that for a normal distribution: 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), 95% lies within 2 standard - deviations of the mean ($\mu\pm2\sigma$), and 99.7% lies within 3 standard - deviations of the mean ($\mu\pm3\sigma$). The mean of a normal distribution divides the data in half (50% of the data is below the mean).

Step2: Calculate the values for 68% interval

Given $\mu = 30$ and $\sigma=2.5$.
The lower bound for the 68% interval is $\mu-\sigma=30 - 2.5=27.5$.
The upper bound for the 68% interval is $\mu+\sigma=30 + 2.5=32.5$.

Step3: Calculate the values for 95% interval

The lower bound for the 95% interval is $\mu - 2\sigma=30-2\times2.5=30 - 5 = 25$.
The upper bound for the 95% interval is $\mu + 2\sigma=30+2\times2.5=30 + 5 = 35$.

Step4: Calculate the values for 99.7% interval

The lower bound for the 99.7% interval is $\mu-3\sigma=30-3\times2.5=30 - 7.5 = 22.5$.
The upper bound for the 99.7% interval is $\mu + 3\sigma=30+3\times2.5=30 + 7.5 = 37.5$.

Step5: Calculate the value for 50%

Since the mean of a normal distribution divides the data in half, 50% of the testing times are below $\mu = 30$.

Answer:

68% of testing times were between 27.5 minutes and 32.5 minutes.
95% of testing times were between 25 minutes and 35 minutes.
99.7% of testing times were between 22.5 minutes and 37.5 minutes.
50% of testing times were below 30 minutes.