Question

Battery packs in electric go-carts need to last a fairly long time. The run-times (time until it needs to be recharged) of the battery packs made by a particular company are Normally distributed with a mean of 2 hours and a standard deviation of 0.33 hour (i.e., 20 minutes). Battery packs that have a run-time in the highest 10% of the run-time distribution are highly sought-after by go-cart drivers. What is the minimum level for which the battery pack will be classified as highly sought-after class

Answer 1

Answer:

The minimum level for which the battery pack will be classified as highly sought-after class is 2.42 hours

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:

$\mu = 2, \sigma = 0.33$

What is the minimum level for which the battery pack will be classified as highly sought-after class

At least the 100-10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

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

$1.28 = \frac{X - 2}{0.33}$

$X - 2 = 0.33*1.28$

$X = 2.42$

The minimum level for which the battery pack will be classified as highly sought-after class is 2.42 hours