The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 30,000 miles

Probability of (x > 30,000) = 0.97725  

Explanation:

Given:

Mean distribution (μ ) = 40,000

Standard deviation (σ ) = 5,000

Raw score of x = 30,000

Computation:

Probability ( x > 30,000 ) = Probability [z > (Raw score of x - Mean distribution ) / Standard deviation]

Probability ( x > 30,000 ) = Probability [z > (30,000 - 40,000) / 5,000]

Probability ( x > 30,000 ) = Probability [z > 2]

Using Z score calculator:

Probability of (x < 30,000) = 0.02275  

So , Probability of (x >30,000) = 1 - 0.02275

Probability of (x > 30,000) = 0.97725