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Which of the following is not​ true? Choose the correct answer below. A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent​ z-score in the standard normal distribution. B. A​ z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. C. A​ z-score is an area under the normal curve. D. If values are converted to standard​ z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution.

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Answer:

A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent​ z-score in the standard normal distribution - false

B. A​ z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution - True

Step-by-step explanation:

A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent​ z-score in the standard normal distribution- This statement is false in the sense that it is a point that is equivalent to corresponding point of normal distribution.

B. A​ z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.  - This statement is true in the sense that z-score is in the normal standard distribution.

C. A​ z-score is an area under the normal curve - This statement is true in the sense that z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.

D. If values are converted to standard​ z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution - This statement is absolutely true

Using concepts of the normal distribution, it is found that the statement which is not true is:

C. A​ z-score is an area under the normal curve.

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]

  • The standard normal distribution has [tex]\mu = 0, \sigma = 1[/tex]. The z-score converts any distribution a standard normal.
  • 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 area under the normal curve.

Thus, statement C is false, as the p-value is the area under the normal curve, not the z-score.

A similar problem is given at https://brainly.com/question/14243195

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