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Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z >d) = 0.6751 , find d.

User Wxtry
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Final answer:

To find the z-score where P(z >d) = 0.6751, subtract this value from 1 to get P(z < d), and then look up this value in the Z-table. The corresponding z-score is roughly -0.44.

Step-by-step explanation:

The student is asking how to find the z-score (d) when given the probability that P(z > d) = 0.6751 in a standard normal distribution.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

To find the z-score that corresponds to P(z > d), we can look up the complementary probability in the z-table, which is P(z < d) because P(z < d) + P(z > d) = 1 for any continuous distribution.

Given that P(z > d) = 0.6751, we find P(z < d) = 1 - 0.6751 = 0.3249.

Now, we use the Z-table to locate the area closest to 0.3249 under the curve to the left of the Z-score.

The z-score that corresponds to this area is approximately d = -0.44.

User Seraphis
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