Question

A normal score is the expected​ z-score of a data​ value, assuming the distribution of the random variable is normal. Is this statement true or​ false? Choose the correct answer below. A.The statement is true. B. The statement is false. The normal score is another name for the​ z-score of a data value. C. The statement is false. The normal score is the area under the normal curve to the left of a​ z-score. D. The statement is false. A normal score is the​ z-score of a data value before it is standardized."

Answer 1

The statement is false; a normal score is another term for the z-score of a data value, not the expected z-score. Z-scores standardize data points to a mean of 0 and standard deviation of 1, and can be interpreted using a z-table to find the cumulative probability.

Step-by-step explanation:

The statement that a normal score is the expected ​z-score of a data​ value, assuming the distribution of the random variable is normal, is false. The correct definition of a normal score is actually another name for the​ z-score of a data value. It is the standardization of a data point within the context of the data set's mean and standard deviation, converted to a standard normal distribution with a mean of 0 and standard deviation of 1.

Z-scores are useful because they allow for comparison across different data sets with differing means and standard deviations by converting the scores to a common scale. A z-score is calculated using the formula ​(z)(o) = x − μ, implying that for a datum x with a mean µ and standard deviation o, the z-score indicates the number of standard deviations it is from the mean.

To interpret z-scores, one would reference a z-table, which lists the cumulative probability (the area under the standard normal curve) to the left of a z-score. This allows us to find probabilities and make statistical inferences based on the standardized data.

Answer 2

In the given case B. The statement is false. A normal score is another name for the​ z-score of a data value.

Step-by-step explanation:

Normal score and z score are often used interchangeably. Both terms refer to a statistical measure indicating how many standard deviations a particular data point is from the mean of a distribution. A z score or normal score helps assess the relative position of a data point within a dataset.

Thus, for the given case, the statement is false. A normal score is another name for the​ z-score of a data value. The normal score is not the expected​ z-score of a data​ value, assuming the distribution of the random variable is normal. The expected​ z-score would be 0, representing the mean of the standard normal distribution.