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sweet [91]
3 years ago
11

The average runtime of a Macbook air is 6 hours with standard deviation 1 hour. Now suppose the frequency distribution of the ru

ntime of all Macbook airs is known to be bell shaped. What percentage approximate all Macbook airs run for less than 5 hours?Group of answer choices20.5%84%54%16%
Mathematics
1 answer:
Dmitrij [34]3 years ago
3 0

Answer:

16%

Step-by-step explanation:

Problems of normally distributed (bell-shaped) samples can be 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 = 6, \sigma = 1

What percentage approximate all Macbook airs run for less than 5 hours?

This is the pvalue of Z when X = 5. So

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

Z = \frac{5 - 6}{1}

Z = -1

Z = -1 has a pvalue of 0.1587

Rounding up, 16% is the correct answer.

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