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%.
Answer: 16%
Step-by-step explanation:
Let the mean of the population of tires denoted by [tex]\mu[/tex] and standard deviation as [tex]\sigma[/tex].
Given : A set of tires is designed to last 6 years, with a standard deviation of 2 years.
i.e. [tex]\mu=6[/tex] and [tex]\sigma=2[/tex]
Let x be the random variable that represents the life of tires.
Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]
For x = 4 , we have
[tex]\dfrac{4-6}{2}=-1[/tex]
Now by using standard normal distribution table we have,
The probability that a tire will last less than 4 years will be :-
[tex]P(x<4)=P(z<-1)= 0.1586553\approx0.16=16\%[/tex]
Hence, the probability that a tire will last less than 4 years = 16%
