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What specific (exact) Z-scores contain the middle 95% of the normal distribution?

A. Between -1.96 and 1.96
B. Between -2.33 and 2.33
C. Between -3.00 and 3.00
D. Between -1.64 and 1.64

Answer :

Final answer:

The exact Z-scores that contain the middle 95% of the normal distribution are between -1.96 and 1.96, which is answer a). This is in accordance with the empirical rule or the 68-95-99.7 rule.

Explanation:

The specific Z-scores that contain the middle 95% of the normal distribution are between -1.96 and 1.96. Therefore, the correct answer is a) Between -1.96 and 1.96. This range is based on the empirical rule, also known as the 68-95-99.7 rule, which states that about 68 percent of values lie between Z-scores of -1 and 1, about 95 percent lie between Z-scores of -1.96 and 1.96, and about 99.7 percent lie between Z-scores of -3 and 3. These Z-scores can be verified by looking up the corresponding area in a Z-table and ensuring that the area between -1.96 and 1.96 is approximately 0.95 or 95%.

Options b) between -2.33 and 2.33 and d) between -1.64 and 1.64 both contain more or less than 95% of the distribution, respectively. Option c) between -3.00 and 3.00 pertains to 99.7% of the distribution. Thus, for the middle 95%, the Z-scores -1.96 and 1.96 are accurate, as they coincide with the standard deviation markers used in the empirical rule.

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