Question

A set of tires is designed to last 6 years, with a standard deviation of 2 years. What is the probability that a tire will last less than 4 years?
1%
10%
16%
26%

Answer 1

Answer: 16%

Step-by-step explanation:

Let the mean of the population of tires denoted by $\mu$  and standard deviation as $\sigma$.

Given : A set of tires is designed to last 6 years, with a standard deviation of 2 years.

i.e.  $\mu=6$  and $\sigma=2$

Let x be the random variable that represents the life of tires.

Z-score : $\dfrac{x-\mu}{\sigma}$

For x = 4 , we have

$\dfrac{4-6}{2}=-1$

Now by using standard normal distribution table we have,

The probability that a tire will last less than 4 years will be :-

$P(x$

Hence, the probability that a tire will last less than 4 years = 16%

Answer 2

Answer:

16%.

Step-by-step explanation:

We may assume that the times are normally distributed.

We first find the z-score which is the (value - mean) / standard deviation.

z-score =  (4 - 6)/2 = -1.

Looking up the value for -1 on a z-score normal distribution table we find that -1 gives us 0.1587  - that is 16%.