A random sample of 40 PCC students are surveyed about their commuting time. A mean of 24.5 minutes was calculated from the survey. The popul

Question

A random sample of 40 PCC students are surveyed about their commuting time. A mean of 24.5 minutes was calculated from the survey. The population standard deviation is known to be 5.8 minutes. Construct a 95% confidence interval for the average commuting time for all PCC students. Round your answer to the nearest tenth of a minute.

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Emery 2 weeks 2022-01-06T08:41:36+00:00 1 Answer 0 views 0

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    2022-01-06T08:43:30+00:00

    Answer:

    [22.7, 26.3]

    Step-by-step explanation:

    -Given that n=40, mean=24.5 and the standard deviation is 5.8.

    -The 95% confidence interval can be calculated as follows:

    CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

    #Substitute the given values to solve for CI:

    CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\\\=24.5\pm1.96\times \frac{5.8}{\sqrt{40}}\\\\\\=24.5\pm 1.8\\\\=[22.7,\ \ \ 26.3]

    Hence, the confidence interval is [22.7, 26.3]

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