Stat homework help

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.2 years, and standard deviation of 3.1 years.

If you randomly purchase one item, what is the probability it will last longer than 16 years?

so i tried to solve by dividing (14/3.1) and i got 4.58064515 and its wrong how would i find that on a z score table?)))

Answer 1

compute the z-statistic (x - mean) / SD, where x = 16, mean = 14.2, SD = 3.1.

z = ( 16 - 14.2 )/3.1 = 0.58

Since want to find P(x > 16), find P(z > 0.58).

Since normal distribution is symmetric, that is the same as P(z < -0.58) = 0.281.