Question

Run a mile During World War II, $12,000$ able bodied male undergraduates at the University of Illinois participated in required physical training. Each student ran a timed mile. Their times followed the Normal distribution with mean 7.11 minutes and standard deviation 0.74 minute. An SRS of 100 of these students has mean time $\overline{x}=7.15$ minutes. A second SRS of size 100 has mean $\overline{x}=6.97$ minutes. After many SRSs, the values of the sample mean $\overline{x}$ follow the Normal distribution with mean $7.11 \mathrm{minutes}-$ and standard deviation 0.074 minute. (a) What is the population? Describe the population distribution. (b) Describe the sampling distribution of $\overline{x} .$ How is it different from the population distribution?

          Run a mile During World War II, $12,000$ able bodied male undergraduates at the University of
Illinois participated in required physical training. Each student ran a timed mile. Their times followed
the Normal distribution with mean 7.11 minutes and standard deviation 0.74 minute. An SRS of 100 of these students has mean time $\overline{x}=7.15$ minutes. A second SRS of size 100 has mean $\overline{x}=6.97$ minutes. After many SRSs, the values of the sample mean $\overline{x}$ follow the Normal distribution with mean $7.11 \mathrm{minutes}-$ and standard deviation 0.074 minute.
(a) What is the population? Describe the population distribution.
(b) Describe the sampling distribution of $\overline{x} .$ How is it different from the population distribution?

Added by Melanie L.

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