Question

The average time it takes a group of senior high school students to

complete a certain examination is 46.2 minutes. The standard deviation is

8 minutes. Assume that the variable is normally distributed.

What is the probability that a random selected college student will

complete the examination in less than 43 minutes?

Answer 1

Suppose that $X$ is a random variable that has a normal distribution with parameters $\mu=46.2$ and $\sigma=8$. The respective probability density function is: $p(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac12\left(\frac{x-\mu}{\sigma}\right)^2}$. The aim is to find $P(X\leq43)$. We receive: $P(X\leq43)=\int_{-\infty}^{43}\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac12\left(\frac{x-\mu}{\sigma}\right)^2}dx\approx0.3446$ (it is rounded to $4$ decimal places)

Answer: $0.3446$ (it is rounded to $4$ decimal places)