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Use the standard normal table to find the $z$-score that corresponds to the cumulative area 0.3669 . If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the $z$-score halfway between the corresponding z-scores.

Click to view page 1 of the standard normal table. Click to view page 2 of the standard normal table.
$z=\square$ (Type an integer or decimal rounded to two decimal places as needed.)
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Step 1 ：The question is asking for the z-score that corresponds to the cumulative area 0.3669 in a standard normal distribution. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The z-score is a measure of how many standard deviations an element is from the mean. In this case, we need to find the z-score such that the area under the curve to the left of that z-score is 0.3669.

Step 2 ：Since we don't have the standard normal table here, we can use the scipy library in Python which provides several functions to work with the normal distribution, including the Percent Point Function (ppf) which is the inverse of the Cumulative Distribution Function (cdf). The ppf takes a probability and returns the corresponding z-score.

Step 3 ：The z-score that corresponds to the cumulative area 0.3669 in a standard normal distribution is approximately -0.34. This means that approximately 36.69% of the data in a standard normal distribution is less than -0.34 standard deviations below the mean.

Step 4 ：Final Answer: \(\boxed{-0.34}\)