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 between 30,000 and 50,000 kilometres?
A)0.5000
B)0.4772
C)0.9544
D)0.9772
E)1.0000

Question

Quizplus · Accepted Answer

First, we need to standardize the values using the formula (X - mean) / standard deviation.
So for 30,000 kilometres, the standardized value would be (30,000 - 40,000) / 5000 = -2.
For 50,000 kilometres, the standardized value would be (50,000 - 40,000) / 5000 = 2.
Next, we need to find the probability of a tire having a life between -2 and 2 using a standard normal distribution table.
The probability of Z being between -2 and 2 is 0.9544.
Therefore, the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 kilometres is 0.9544.

Sure Stone Tire Company Has Established That the Useful Life