Respuesta :
Assuming that the variable Z is denoting standard normal variate, we get its probability as given by: Option A: 0.0179
How to get the z scores?
If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For the given case, we need to find out the probability of P(Z < -2.1)
Using the z-tables(available online), we get the p-value for Z = -2.1 as:
Thus, we get the needed probability as:
[tex]P(Z < -2.1) = P(Z \leq -2.1) = 0.0179[/tex]
Thus, assuming that the variable Z is denoting standard normal variate, we get its probability as given by: Option A: 0.0179
Learn more about z-scores here:
https://brainly.com/question/21262765
