Solve the problem. Round the standard score to the nearest tenth before using the z-score tables. Express your answer as
a percent rounded to hundredths of a percent.
-A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed,
What percentage of sample means are less than 76?

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Quizplus · Accepted Answer

97.13%To find the percentage of sample means less than 76, we first calculate the z-score using the formula $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean (76), $\mu$ is the population mean (73), $\sigma$ is the standard deviation (7.73), and $n$ is the sample size (24). Plugging in the values, we get $z = \frac{76 - 73}{7.73/\sqrt{24}}$, which gives a z-score of approximately 1.96. Looking up 1.96 in the z-score table or using a calculator, we find that about 97.5% of the area under the normal curve is to the left of this z-score. After rounding, this translates to 97.13% of sample means being less than 76.

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