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3.
The probability that a standardized normal random variable, Z, is less than 50 is
approximately 0.
A) True
B) False

Respuesta :

A) True
Hope this helps you out!

Using the normal distribution, it is found that this statement is False, hence option B is correct.

Normal Probability Distribution

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • 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, we have a standard normal variable, which means that [tex]\mu = 0, \sigma = 1[/tex].

The probability that it is less than 50 is the p-value of Z when X = 50, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{50 - 0}{1}[/tex]

[tex]Z = 50[/tex]

[tex]Z = 50[/tex] has a p-value of 1.

The probability is approximately 1, hence the statement is False and option B is correct.

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

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