Question

The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the probability that a computer will take more than 42 seconds to boot up?

Answer 1

0.008 is the probability that a computer will take more than 42 seconds to boot up.

Explanation:

We are given the following information in the question:

Mean, μ = 30 seconds

Standard Deviation, σ = 5 second

We are given that the distribution of time taken for a computer to boot up is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P(computer will take more than 42 seconds to boot up)

P(x > 42)

`P( x > 42) = P( z > \displaystyle(42 - 30)/(5)) = P(z > 2.4)`

`= 1 - P(z \leq 2.4)`

Calculation the value from standard normal z table, we have,

`P(x > 42) = 1 - 0.992 = 0.008`

0.008 is the probability that a computer will take more than 42 seconds to boot up.