Given that the z is a standard normal random variable, what is the value of z if the area to the left of z is .9382?
To find the value of z for a given area under the standard normal curve, we can use a standard normal distribution table or a calculator
To find the value of z for a given area under the standard normal curve, we can use a standard normal distribution table or a calculator.
In this case, where the area to the left of z is 0.9382, we need to find the z-score that corresponds to this area.
A standard normal distribution table typically provides the z-scores corresponding to areas to the left of the z-score. However, in this case, the given area (0.9382) is not listed directly in the table.
To find the closest z-score, we can use a process called inverse normal calculation or z-score calculation.
Using a calculator (or specialized software), we can perform an inverse normal calculation to find the z-score corresponding to the area of 0.9382. This z-score is usually denoted as zα.
Using a calculator or software, we find that the z-score zα ≈ 1.8264 (rounded to four decimal places)
Therefore, the value of z such that the area to the left of z is 0.9382 is approximately 1.8264.
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