64 lines
1.6 KiB
Plaintext
64 lines
1.6 KiB
Plaintext
<section xml:id="sec-CLT" xmlns:xi="http://www.w3.org/2001/XInclude">
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<title>Central Limit Theorem</title>
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<p>
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Text of section.
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</p>
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<exercises xml:id="exercises-CLT">
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<exercise>
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<statement>
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<p>
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Suppose a coin has probability 0.4 of coming up heads, and we flip the coin 100 times.
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Let <m>S</m> be the number of heads.
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Estimate the probability that <m>34 \leq S \leq 44</m>.
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</p>
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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Suppose a fair die is rolled 100 times, and let <m>m</m> be the average value of the rolls.
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Estimate the probability that <m>3.45 \leq m \leq 3.55</m>.
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</p>
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</statement>
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</exercise>
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<exercise>
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<introduction>
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<p>
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The heights of men in the US have a mean of 69 in and a variance of about 9 in<m>^2</m>, and the heights of women in the US have a mean of 63.5 in with a variance of 6.25 in<m>^2</m>.
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</p>
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</introduction>
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<task>
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<statement>
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<p>
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Suppose the heights of 30 men are sampled, and a sample mean <m>m</m> is taken.
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Find the expected value and variance of <m>m</m>.
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Estimate the probability that <m>m \geq 69.5</m>.
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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What if the sampled group was women?
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</p>
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</statement>
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</task>
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</exercise>
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</exercises>
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</section> |