Determine the two z-scores that separate the middle 96% of the distribution from the area in the tails of the standard normal distribution.

Z = -2.054 and Z = 2.054

Step-by-step explanation:

Z-score:

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 96%

The normal distribution is symmetric, so:

From the: 50 - (96/2) = 2nd percentile

To the: 50 + (96/2) = 98th percentile

2nd percentile:

Z with a pvalue of 0.02. So Z = -2.054.

98th percentile:

Z with a pvalue of 0.98. So Z = 2.054.

Z = -2.054 and Z = 2.054

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