SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.9 years, and standard deviation of 3.1 years. The 4% of items with the shortest life

Algebra ->  Statistics  -> Central-limit-theorem -> SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.9 years, and standard deviation of 3.1 years. The 4% of items with the shortest life      Log On


   



Question 1145360: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.9 years, and standard deviation of 3.1 years.
The 4% of items with the shortest lifespan will last less than how many years?

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Go to a z-table and find the value that corresponds with a score of 0.04. The closest z-score is -1.75.

%28x+-+9.9%29%2F3.1+=+-1.75

Cross-multiply:

x - 9.9 = -5.425

x = 4.475

The 4% with the lowest lifespan will last less than 4.475 years.