Question

A normal distribution (X) has a mean of 100 and a standard deviation of 10.

What is the probability that X will be smaller than 80?

Use the Normal Table and keep all 4 decimal positions in your answer.

Answer 1

Using the normal distribution, it is found that there is a 0.0228 = 2.28% probability that X will be smaller than 80.

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 $\mu = 100$.

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

The probability that X will be smaller than 80 is the p-value of Z when X = 80, hence:

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

$Z = \frac{80 - 100}{10}$

$Z = -2$

$Z = -2$ has a p-value of 0.0228.

0.0228 = 2.28% probability that X will be smaller than 80.

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