To find the z value for P(Z<=z) = 0.8914, you would look up the value 0.8914 in the standard normal distribution table. The closest value to this probability is 0.8915, which corresponds to a z value of approximately 1.25.
To find the z value for P(Z>z) = 0.8001, you would first find the value for P(Z<=z) by subtracting this probability from 1. So P(Z<=z) = 1 - 0.8001 = 0.1999. Looking up this value in the table, the closest value is 0.1998, which corresponds to a z value of approximately -0.90. Therefore, the z value for P(Z>z) = 0.8001 is approximately -0.90.
To find the z values for P(-z<=Z<=z) = 0.94, you would find the corresponding area for the tail probabilities at both ends and then subtract them from 0.94. The tail probability is (1 - 0.94)/2 = 0.03, so each end would have a tail probability of 0.03. Looking up the tail probability of 0.03 in the table, the closest value is 0.0294, which corresponds to a z value of approximately 1.88 (positive end) and -1.88 (negative end). Therefore, the z values for P(-z<=Z<=z) = 0.94 are approximately -1.88 and 1.88.
To find the z value for P(0<=Z<=z) = 0.4067, you would subtract the probability at the lower end (0) from the given probability. So, P(Z<=z) = 0.4067 - 0 = 0.4067. Looking up this value in the table, the closest value is 0.4082, which corresponds to a z value of approximately 1.20. Therefore, the z value for P(0<=Z<=z) = 0.4067 is approximately 1.20.
Find the following z values for the standard normal variable Z. (You may find it useful to reference the z table. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
P(Z<=z)=0.8914
P(Z>z)=0.8001
P(-z<=Z<=z)=0.94
P(0<=Z<=z)=0.4067
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