Question

1. Data are from a normal distribution and the mean is 20 with a standard deviation of 2. a. What % of observations fall between 18 and 22

Answer 1

Answer:

$P(18$

And we can find this probability with the normal standard distribution and we got:

$P(-1$

Step-by-step explanation:

Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:

$X \sim N(20,2)$  

Where $\mu=20$ and $\sigma=2$

We are interested on this probability

$P(18$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

Using this formula we got:

$P(18$

And we can find this probability with the normal standard distribution and we got:

$P(-1$