Question

A normal distribution has a mean of 10 and a standard

Answer 1

Answer:

15.87% probability of selecting a number that is at most 9

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 10, \sigma = 1$

What is the probability of selecting a number that is at most 9?

This is the pvalue of Z when X = 9. So

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

$Z = \frac{9 - 10}{1}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

15.87% probability of selecting a number that is at most 9