Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 kilometres and a standard deviation of 5000 kilometres.What is the probability that a randomly selected tire of this brand has a life of at most 30,000 kilometres?
A)0.5000
B)0.4772
C)0.0228
D)0.9772
E)1.0000

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly selected tire has a life of at most 30,000 km. This can be calculated using the standard normal distribution as follows:
Z = (X - μ) / σ 
where X is the value we want to find the probability for (30,000 km), μ is the mean (40,000 km), and σ is the standard deviation (5000 km).
Substituting the values, we get:
Z = (30,000 - 40,000) / 5000 = -2
Using a standard normal distribution table or calculator, we can find the probability that Z is less than or equal to -2, which is 0.0228. Therefore, the probability that a randomly selected tire has a life of at most 30,000 km is 0.0228 or 2.28%. The best choice is C.

Sure Stone Tire Company Has Established That the Useful Life