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Suppose a population is normally distributed with a mean [tex] \mu = 116 [/tex] and a standard deviation [tex] \sigma = 14 [/tex]. Approximately what percent of the population would be between 116 and 130?

Answer :

Final answer:

To find the percent of the population between 116 and 130, calculate the z-scores for these values and use the z-table to find the corresponding percentiles.

Explanation:

To find the percent of the population between 116 and 130, we need to calculate the z-scores for these values and then use the z-table to find the corresponding percentiles. The formula for calculating the z-score is: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For the value 116: z = (116 - 116) / 14 = 0

For the value 130: z = (130 - 116) / 14 ≈ 1

Using the z-table, we can find that approximately 68% of the population is within one standard deviation of the mean, which means that approximately 34% is between the mean and one standard deviation above the mean. Since 130 is one standard deviation above the mean, we can estimate that approximately 34% - 50% = 16% of the population is between 116 and 130.

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