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?

a) 0.6915; b) 2.83 years

Step-by-step explanation:

For part a,

The formula for a z score is

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.

5x+10 is the correct one

hope this

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.