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Answer :
For the normal distribution rule, we're looking for a z-value with less than 90% to its left, corresponding to an upper tail greater than 10%. The closest z-score provided that meets this criterion is 0.8.
The 68-95-99.7 empirical rule, also known as the normal distribution rule, states that approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
To find which z-value has an upper tail of more than 10%, we need to look for a z-value that corresponds to the body (to the left) being less than 90% because the body percent and the tail percent add up to 100%.
Considering the choices given, a z-score of 1.28 corresponds closely to an upper tail of 10% (because the body to the left is about 90%), and out of the provided options, z = 1.34 (choice b) is the closest to this value without going over.
Therefore, the correct answer is b) 0.8.
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