We can use the normal distribution formula to calculate the probability that a tire of this brand will last longer than 57,300 miles:
z = (x - μ) / σ
where x is the value we want to find the probability for (in this case, 57,300 miles), μ is the mean of the distribution (60,000 miles), and σ is the standard deviation of the distribution (2700 miles). z is the standardized value of x that we can use to look up the probability in a standard normal distribution table.
Substituting the values we have, we get:
z = (57,300 - 60,000) / 2700
z = -1
Looking up the probability of a standard normal distribution table for z = -1, we get:
P(Z > -1) = 0.8413
where Z is the standard normal distribution.
Therefore, the probability that a tire of this brand will last longer than 57,300 miles is approximately 0.8413, or 84.13%.