for a certain psychiatric evaluation z scores above 2.18 and below -2.33 are considered abnormal. what is the probability that a person evaluated by this will be considered normal?
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To find the probability that a person evaluated will be considered normal, we need to determine the area under the standard normal distribution curve between the z-scores of -2.33 and 2.18.
Step 1: Convert the z-scores into corresponding cumulative probabilities using a standard normal distribution table or a calculator.
The z-score of -2.33 corresponds to a cumulative probability of approximately 0.0099. (You can use a standard normal distribution table or a calculator to find this.)
The z-score of 2.18 corresponds to a cumulative probability of approximately 0.9857.
Step 2: Find the probability between these two cumulative probabilities.
To find the desired probability, we subtract the cumulative probability of -2.33 from the cumulative probability of 2.18:
P( -2.33 < z < 2.18 ) = 0.9857 - 0.0099 = 0.9758
Therefore, the probability that a person evaluated by this psychiatric evaluation will be considered normal is 0.9758 or approximately 97.58%.
Note: This assumes that the distribution of the psychiatric evaluation scores follows a normal distribution.