Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. To the nearest integer, how many values are between 87 and 99?

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Quizplus · Accepted Answer

To find the number of values between 87 and 99 in a normally distributed population, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 87, Z = (87 - 90) / 6 = -0.5. For X = 99, Z = (99 - 90) / 6 = 1.5. Looking these Z-scores up in a standard normal distribution table, the area between Z = -0.5 and Z = 1.5 is approximately 0.624. Multiplying this by the total population (0.624 * 900) gives approximately 562 values.

Consider a Population of 900 Values That Are Normally Distributed