Answer :
Z-value 0.8 has an upper tail area greater than 0.1 (or 10%) according to the Empirical Rule, as it's less than the z-score of 1.96, which corresponds to upper tail areas less than 10%. Therefore the correct option is a.
The question is asking which z-value corresponds to an upper tail area that exceeds 0.1 (or 10%) using the 68-95-99.7 Empirical Rule, also known as the normal distribution. The Empirical Rule states that approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations in a normal distribution.
For z-values corresponding to an upper tail area greater than 0.1, we need a z-value which corresponds to less than 90% of the data below it, since 100% - 10% (upper tail) = 90% (below). According to the empirical rule, 95% of the data falls between z-scores of -1.96 and 1.96. Therefore, we can conclude that the z-value 0.8 (a) would have more than 10% in the upper tail since it is less than 1.96.
The other options, b) 2.5, c) 2.1, and d) 3.8, would all have upper tail areas less than 10% since they are greater than z = 1.96, which corresponds to 2.5% in the upper tail (one-sided).
