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taurus [48]
2 years ago
13

Dots sells a total of 266 T-shirts ($2) and shorts ($4). In April, total sales were $672.

Mathematics
1 answer:
Anit [1.1K]2 years ago
4 0
T-Shirts: 158
Shorts: 107
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The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 mi
dem82 [27]

Answer:

62.17% probability that a randomly selected exam will require more than 15 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 = 16.3, \sigma = 4.2

What is the probability that a randomly selected exam will require more than 15 minutes to grade

This is 1 subtracted by the pvalue of Z when X = 15. So

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

Z = \frac{15 - 16.3}{4.2}

Z = -0.31

Z = -0.31 has a pvalue of 0.3783.

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62.17% probability that a randomly selected exam will require more than 15 minutes to grade

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Step-by-step explanation:

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