Question

the time to complete an exam is approximately normal with a mean \\( \mu = 50 \\) minutes and a standard deviation \\( \sigma = 3 \\) 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. \\( \mu = 50 \\) \\( \sigma = 3 \\) \\( \mu - 3\sigma \\) \\( \mu - 2\sigma \\) \\( \mu - \sigma \\) \\( \mu \\) \\( \mu + \sigma \\) \\( \mu + 2\sigma \\) \\( \mu + 3\sigma \\) question help: video message instructor submit question jump to answer

Explanation:

Step1: Calculate \(\mu - 3\sigma\)

Given \(\mu = 50\) and \(\sigma=3\), then \(\mu - 3\sigma=50 - 3\times3=50 - 9 = 41\)

Step2: Calculate \(\mu - 2\sigma\)

\(\mu - 2\sigma=50-2\times3 = 50 - 6=44\)

Step3: Calculate \(\mu-\sigma\)

\(\mu-\sigma=50 - 3=47\)

Step4: Calculate \(\mu\)

\(\mu = 50\)

Step5: Calculate \(\mu+\sigma\)

\(\mu+\sigma=50 + 3=53\)

Step6: Calculate \(\mu + 2\sigma\)

\(\mu + 2\sigma=50+2\times3=50 + 6 = 56\)

Step7: Calculate \(\mu+3\sigma\)

\(\mu+3\sigma=50+3\times3=50 + 9=59\)

Answer:

41, 44, 47, 50, 53, 56, 59