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Assume the random variable x is normally distributed with a mean of 82 and a standard deviation of 4.

Find the indicated probability P(x<80).

User Eric Ahn
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Final answer:

To find the probability P(x<80), convert the value to a Z-score and use a Z-table to find the area to the left of the Z-score. The probability is approximately 30.85%.

Step-by-step explanation:

To find the probability P(x<80), we need to standardize the value of 80 using the Z-score formula. The Z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. In this case, the Z-score is calculated as (80 - 82) / 4 = -0.5. We can then use a Z-table or a calculator to find the area to the left of the Z-score.

Looking up the Z-score -0.5 in a Z-table, we find that the area to the left of the Z-score is approximately 0.3085. Therefore, the probability P(x<80) is approximately 0.3085 or 30.85%.

User Joe Ratzer
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