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Flauer [41]
3 years ago
13

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a s

tandard deviation of 2.5 minutes. What is the probability that randomly selected homework will require between 8 and 12 minutes to grade?
Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0

Answer:

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 12.6, \sigma = 2.5

What is the probability that randomly selected homework will require between 8 and 12 minutes to grade?

This is the pvalue of Z when X = 12 subtracted by the pvalue of Z when X = 8. So

X = 12

Z = \frac{X - \mu}{\sigma}

Z = \frac{12 - 12.6}{2.5}

Z = -0.24

Z = -0.24 has a pvalue of 0.4052

X = 8

Z = \frac{X - \mu}{\sigma}

Z = \frac{8 - 12.6}{2.5}

Z = -1.84

Z = -1.84 has a pvalue of 0.0329

0.4052 - 0.0329 = 0.3723

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

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