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If the probability of getting a z-score between the mean of +1 standard deviation is 0.3413, what is the probability of getting a z-score of +1 standard deviation or less?Choose one0.34130.15870.65870.8413

Question

If the probability of getting a z-score between the mean of +1 standard deviation is 0.3413, what is the probability of getting a z-score of +1 standard deviation or less?Choose one0.34130.15870.65870.8413

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Solution

The probability of getting a z-score of +1 standard deviation or less is 0.8413.

Here's why:

The Z-score of +1 standard deviation means that the value is one standard deviation above the mean. The probability of getting a value at the mean (Z-score of 0) is 0.5 (or 50%) because the mean splits the data into two equal halves.

The question states that the probability of getting a z-score between the mean and +1 standard deviation is 0.3413 (or 34.13%). This is the area under the curve of the normal distribution between the mean and one standard deviation above the mean.

To find the probability of getting a z-score of +1 standard deviation or less, you add the probability of getting a value at the mean (0.5) and the probability of getting a z-score between the mean and +1 standard deviation (0.3413).

So, 0.5 (probability at the mean) + 0.3413 (probability between the mean and +1 standard deviation) = 0.8413 (or 84.13%).

Therefore, the probability of getting a z-score of +1 standard deviation or less is 0.8413.

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