The scores on a college entrance exam is 100 with a standard deviation of 7.5. How do you find the probability that a randomly selected score is between 85 and 100?

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Answer 1 · 2017-06-22T14:37:30

Proability that a randomly selected score is between $85$ $85$ and $100$ $100$ is $47.72 %$ $47.72%$

Asumming that the distribution is normal, let us find the $z$ $z$ score of $85$ $85$ and $100$ $100$ .

As $μ = 100$ $mu=100$ and $σ = 7.5$ $sigma=7.5$

$z$ $z$ -score is given by $\frac{x - μ}{σ}$ $(x-mu)/sigma$

Hence for $85$ $85$ , $z$ $z$ -scorre is $\frac{85 - 100}{7.5} = - \frac{15}{7.5} = - 2$ $(85-100)/7.5=-15/7.5=-2$

and for $100$ $100$ , $z$ $z$ -scorre is $\frac{100 - 100}{7.5} = 0$ $(100-100)/7.5=0$

Hence area between $- 2$ $-2$ and $0$ $0$ from tables is $0.4772$ $0.4772$

and probability is $47.72 %$ $47.72%$

[See more here.](https://socratic.org/questions/the-area-under-the-normal-curve-between-z-1-0-and-z-2-0#443143)