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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?

Respuesta :

Answer:

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

Step-by-step 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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(more than 4.25 minutes to solve a problem)

[tex]P( x > 4.25) = P( z > \displaystyle\frac{4.25 - 4}{0.25}) = P(z > 1)[/tex]

[tex]= 1 - P(z \leq 1)[/tex]

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

[tex]P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]

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

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