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

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

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

$P(z>0.5)=0.30854$

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

Answer 2

Using the normal distribution, it is found that there is a 0.3085 = 30.85% probability of randomly selecting a score greater than 85 from this distribution.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.

• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

• The mean is of $\mu = 80$.

• The standard deviation is of $\sigma = 10$.

The probability of randomly selecting a score greater than 85 from this distribution is 1 subtracted by the p-value of Z when X = 85, hence:

$Z = \frac{X - \mu}{\sigma}$

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

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% probability of randomly selecting a score greater than 85 from this distribution.

More can be learned about the normal distribution at https://brainly.com/question/24663213