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What is the probability that y is within 1 standard deviation of its mean value?

User Milkovsky
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Final answer:

Approximately 68% of the values in a normal distribution are expected to be within 1 standard deviation of its mean, which is known as the empirical rule.

Step-by-step explanation:

The probability that y is within 1 standard deviation of its mean value in a normal distribution is about 68%. This probability comes from the empirical rule which states that for any normal distribution, approximately 68% of the values will fall within plus or minus 1 standard deviation from the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. Given that the distributions of y values are normally distributed about the line, with the means lying on the line, it's safe to apply this rule.

Therefore, if you are given a normal distribution with a known standard deviation and mean, you can predict that about 68% of the values will lie within one standard deviation above or below the mean.

User Shijil Narayanan
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