Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of 0.8 years. If you randomly purchase one item, what is the probability it will last longer than 14 years

Answer 1

probability of lasting longer = 1.7%

Explanation:

We are given:

x' = 14 years

μ = 12.3 years

s = 0.8 years

Thus, let's use the formula for the Z-score value which is;

z = (x' - μ)/s

Thus;

z = (14 - 12.3)/0.8

z = 2.125

From the z-distribution table attached, the p-value is ;

P(x' > 2.125) = 1 - 0.983 = 0.017 = 1.7%

Thus,probability of lasting longer = 1.7%