Let the random variable Z follow a standard normal distribution,and let z₁ be a possible value of Z that is unknown but identifiable by position and area.Find z₁ if the symmetrical area between a negative z₁ and a positive z₁ is 0.9544. A)2.00 B)0.11 C)2.50 D)0.06

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Quizplus · Accepted Answer

Since the area between a negative z-score and a positive z-score is 0.9544 and the normal distribution is symmetrical, we can find the z-score corresponding to the area (0.9544 + 1)/2 = 0.9772 using a standard normal distribution table or a calculator. Using a standard normal distribution table, we find that the z-score corresponding to an area of 0.9772 is approximately 2.00 (rounding to two decimal places). Therefore, z₁ = 2.00. Alternatively, using a calculator, we can use the inverse normal function to find the z-score corresponding to an area of 0.9772. In Excel, the function is =NORMSINV(0.9772), which also gives a result of approximately 2.00.

Let the Random Variable Z Follow a Standard Normal Distribution,and