Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. What proportion of values in the population are larger than 63?

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Quizplus · Accepted Answer

To find the proportion of values larger than 63 in a normally distributed population, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Plugging in the given values: Z = (63 - 60) / 8 = 3 / 8 = 0.375. Looking up 0.375 in a Z-table or using a normal distribution calculator gives us the proportion of values to the left of 63. Since we want the proportion larger than 63, we subtract this value from 1. The Z-table gives us approximately 0.646 for 0.375, so 1 - 0.646 = 0.354.

Imagine a Population Consisting of 1,500 Values That Are Normally