Question

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

Answer 1

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.