Final answer:
To find the z-score with a right tail probability of 0.054799, one would consult a z-score table or use statistical software since the probability is larger than the one corresponding to the z-value of 1.96. The exact z-score is slightly less than 1.645, as that value corresponds to a right tail probability of about 0.05.
Step-by-step explanation:
The student has asked to find the value of z such that the probability that a standard normal random variable is greater than z is 0.054799. To find this, one would typically use a z-score table or a calculator with inverse normal functions, such as invNorm in a TI-83/84 calculator, or use a statistical software.
Using the critical value reference provided, we know that the critical value 1.96 has 0.025 to its right tail. Since our probability of interest, 0.054799, is greater than 0.025, the corresponding z-value must be less than 1.96. Consulting a more detailed standard normal distribution table or using software for the exact probability will give us the precise z-score.
To estimate, consider that a z-score around 1.645 has a right tail probability of about 0.05. Since 0.054799 is a bit larger, the z value we're looking for is slightly less than 1.645.