Question

Scott is on his school's academic team. On average, it takes Scott 4 minutes, with a standard deviation of 0.25 minutes, to solve a problem at an academic bowl. How often will it take Scott more than 4.25 minutes to solve a problem at an academic bowl?

Answer 1

15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.

Explanation:

We are given the following information in the question:

Mean, μ = 4 minutes

Standard Deviation, σ = 0.25 minutes

We standardize the given data.

Formula:

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

P(more than 4.25 minutes to solve a problem)

`P( x > 4.25) = P( z > \displaystyle(4.25 - 4)/(0.25)) = P(z > 1)`

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

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

`P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%`

Thus,15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.