QuestionA manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.4 years, and standard deviation of 3.9 years.
If you randomly purchase one item, what is the probability it will last longer than 20 years? Please show your answer to 4 decimal places.
Probability $=$ $\square$

Studdy Solution
Calculate the probability that the item lasts longer than 20 years by subtracting the cumulative probability from 1.
$$P(X > 20) = 1 - P(Z \leq 1.9487)$$ $$P(X > 20) = 1 - 0.9744$$ $$P(X > 20) \approx 0.0256$$
Therefore, the probability that a randomly selected item will last longer than 20 years is approximately 0.0256.
Probability $=$ $0.0256$