Question

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean =41 and standard deviation =6
(a) What is the probability that a randomly chosen tire has a lifetime greater than 50 thousand miles?

Answer 1

Answer:

6.68% probability that a randomly chosen tire has a lifetime greater than 50 thousand miles

Step-by-step explanation:

Problems of normally distributed 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:

$\mu = 41, \sigma = 6$

(a) What is the probability that a randomly chosen tire has a lifetime greater than 50 thousand miles?

This is 1 subtracted by the pvalue of Z when X = 50. So

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

$Z = \frac{50 - 41}{6}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

6.68% probability that a randomly chosen tire has a lifetime greater than 50 thousand miles