Question

The usual life of a computer terminal at a university computer center is known to be normally distributed with a mean of 3.25 years and a standard deviation of .5 years. A. What proportion of computer terminals will have a useful life of at least 3 years?B. Historically, 20% of the terminals have had a useful life less than the manufacture's advertised life. What is the manufacture's advertised life for the computer terminals?

Answer 1

a) 0.6915; b) 2.83 years

Explanation:

For part a,

The formula for a z score is

`z=(X-\mu)/(\sigma)`

Our mean, μ, is 3.25 and our standard deviation, σ, is 0.5.

This gives us

z = (3-3.25)/0.5 = -0.25/0.5 = -0.5

Using a z table, we see that the area under the curve to the left of this is 0.3085. However we want the area to the right; this means we subtract from 1:

1-0.3085 = 0.6915

For part b,

We look in the cells of a z table to find the value closest to 20%, or 0.2000. This is 0.2005, which corresponds with a z score of -0.84:

-0.84 = (X-3.25)/0.5

Multiply both sides by 0.5:

0.5(-0.84) = ((X-3.25)/0.5)(0.5)

-0.42 = X-3.25

Add 3.25 to each side:

-0.42+3.25 = X-3.25+3.25

X = 2.83

The advertised life would be 2.83 years.