# The times it takes 5th graders to complete a mathematics problem are Normally distributed with mean 2 min and standard deviation 0.8 min. What is the probability that a randomly chosen 5th grader will take more than 2.5 minutes to complete the problem?

Apr 8, 2017

0.266

#### Explanation:

X ~ N(2, ${0.8}^{2}$)

P (X > 2.5)

= P $\left(Z > \frac{2.5 - 2}{0.8}\right)$

= P $\left(Z > 0.625\right)$

= 1 - $\Phi \left(0.625\right)$

= 1 - 0.734

= 0.266