Consider a population of 900 values that are normally distributed with a mean of 90 and standard deviation of 6. What proportion of values are larger than 78?

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Quizplus · Accepted Answer

To find the proportion of values larger than 78, we first calculate the z-score for 78 using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values, we get $z = \frac{(78 - 90)}{6} = -2$. Looking up a z-score of -2 in the standard normal distribution table or using a calculator, we find that the proportion of values less than 78 is approximately 0.0228. Therefore, the proportion of values larger than 78 is $1 - 0.0228 = 0.9772$.

Consider a Population of 900 Values That Are Normally Distributed