Question

A normal distribution has μ=80 and σ=10. What is the probability of randomly selecting a score greater than 85 from this distribution?

Answer 1

Answer:

$0.30854$ or $30.854\%$.

Step-by-step explanation:

We have been given that a normal distribution has μ=80 and σ=10. We are asked to find the the probability of randomly selecting a score greater than 85 from this distribution.

First of all, we will find the z-score corresponding to normal score 85 as:

$z=\frac{x-\mu}{\sigma}$

Upon substituting our given values in z-score formula, we will get:

$z=\frac{85-80}{10}$

$z=\frac{5}{10}$

$z=0.5$

Now, we need to find $P(z>0.5)$ for the probability of randomly selecting a score greater than 85 from this distribution.

Using formula $P(z>a)=1- P(z$, we will get:

$P(z>0.5)=1-P(z$

$P(z>0.5)=1-0.69146$

$P(z>0.5)=0.30854$

Therefore, the probability of randomly selecting a score greater than 85 from this distribution would be 0.30854 or $30.854\%$.