In a normal distribution, what z-score value separates the highest 90% of the scores from the rest of the distribution?

a)z = -1.28
b)z = 1.28
c)z = -0.13
d)z = 0.13

To find the z-score value that separates the highest 90% of the scores from the rest of the distribution in a normal distribution, you need to look up the corresponding value in the standard normal distribution table.

The standard normal distribution table provides the probability that a random variable, following a standard normal distribution, is less than or equal to a given z-score. Since we want to find the z-score that separates the highest 90% of the scores, we are interested in the area under the curve to the left of this z-score.

The highest 90% of the scores will be the complement of the lowest 10% of the scores. The area to the left of the z-score in question will be equal to 1 minus the probability of the lowest 10%. In terms of the standard normal distribution, we can find the z-score that corresponds to this probability.

Using the standard normal distribution table or a z-score calculator, you can find that the z-score that corresponds to a probability of 0.90 is approximately 1.28.

Therefore, the correct answer is b) z = 1.28.

To find the z-score value that separates the highest 90% of the scores from the rest of the distribution, we need to find the z-score corresponding to the cumulative probability of 0.90.

Using a standard normal distribution, we can determine this value by referring to a z-table or using a statistical calculator.

The closest option is z = 1.28, which corresponds to a cumulative probability of approximately 0.8997. Therefore, the answer is:

b) z = 1.28

Look up the Z scores in the back of your stat text labeled something like "areas under the normal distribution." That should give you the answer.