Answer :
The correct z value with an upper tail probability of less than 0.05, based on the 68-95-99.7 Empirical rule and Standard Normal Distribution Table, is closest to z=1.99 (Option A). Therefore correct option A. 02
The question concerns identifying which z value corresponds to an upper tail probability of less than 0.05, according to the 68-95-99.7 Empirical rule, also known as the empirical rule or the three-sigma rule. This 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, in a normal distribution. When looking for an upper tail probability of less than 0.05, we are looking for the z value that leaves less than 5% of the data above it.
The answer can be found using the Standard Normal Distribution Table. The closest z value to an upper tail probability of 0.05 is typically around z=1.645 for a one-tailed test, but since the z value is not specified among the options (A, B, C, D), we can deduce it from similar facts. For instance, a z value of approximately 1.96 corresponds to an upper tail probability of 0.025 for a two-tailed test, which would be even smaller for a one-tailed test, satisfying the requirement of being less than 0.05. Therefore, the correct z value with an upper tail less than 0.05 would be closest to z = 1.99 (option A). Therefore correct option A. 02
