Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.1 years, and standard deviation of 1.1 years. 

If you randomly purchase one item, what is the probability it will last longer than 3 years?

Answer 1

Given: = 4.1, = 1.1

To find the probability, we need to find the Z scores first.

For P (X > 3) = 1 - P (X < 3), as the normal tables give us the left tailed probability only.

For P( X < 3); Z = (3 – 4.1)/1.1 = -1

The probability for P(X < 3) from the normal distribution tables is = 0.1587

Therefore the required probability = 1 – 0.1587 = 0.8413