Question

The lifetime for a certain type of tre has been shown to be five years the mean) with a standard deviation of 6 months. In a normal distribution, what percentage of these tires will
last more than six years (more than two standard deviations above the mean)?

Answer 1

Answer:

2.28%

Step-by-step explanation:

mean = 5 years = 60 months

standard deviation = 6 months

X = number of years the tires will last

P = probability of ...

z = z-score

6 years = 72 months

z = (# of months - mean) / standard deviation

z = (72 - 60)/6

z = 12/6

z = 2

P(X > 72) = 1 - P(X < 72)

= 1 - P(z < 2)    

(using a Standard Normal Probabilities Table we can see that P(z < 2) = .9772)

So:

= 1 - .9772

= 0.0228 OR 2.28%