Find the z value such that P(−z ≤ Z ≤ z) = 0.866.Multiple Choicez = 1.499z = −1.184z = 1.184z = −1.499
Question
Find the z value such that P(−z ≤ Z ≤ z) = 0.866.
Multiple Choice
- z = 1.499
- z = −1.184
- z = 1.184
- z = −1.499
Solution
The question is asking for the z-value that corresponds to a probability of 0.866 in a standard normal distribution.
The standard normal distribution is symmetric around zero, so if P(-z ≤ Z ≤ z) = 0.866, then P(Z ≤ z) = (0.866 + 1) / 2 = 0.933.
We can find this z-value by looking it up in a standard normal distribution table or using a calculator with a built-in function for the standard normal distribution.
The z-value that corresponds to a probability of 0.933 is approximately 1.499.
So, the correct answer is z = 1.499.
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