Question

which of the following is not true? choose the correct answer below. a. a z - score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. b. a z - score is an area under the normal curve. c. 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. 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.

Explanation:

A z - score is a measure of how many standard deviations an element is from the mean. It is not an area under the normal curve. Areas under the normal curve are probabilities and are found using z - scores, but the z - score itself is a standardized value. Option A is the definition of a z - score. Option C is true because standardizing to z - scores preserves areas. Option D is true as standardizing to z - scores allows us to use the same procedures for all normal distributions as for the standard normal distribution.

Answer:

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