Central Limit Theorem

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Section 4.1 Central Limit Theorem

Text of section.

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Exercises Exercises

1.

Suppose a coin has probability 0.4 of coming up heads, and we flip the coin 100 times. Let $S$ be the number of heads. Estimate the probability that $34 \leq S \leq 44\text{.}$

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2.

Suppose a fair die is rolled 100 times, and let $m$ be the average value of the rolls. Estimate the probability that $3.45 \leq m \leq 3.55\text{.}$

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3.

The heights of men in the US have a mean of 69 in and a variance of about 9 in$^2\text{,}$ and the heights of women in the US have a mean of 63.5 in with a variance of 6.25 in$^2\text{.}$

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(a)

Suppose the heights of 30 men are sampled, and a sample mean $m$ is taken. Find the expected value and variance of $m\text{.}$

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(b)

Estimate the probability that $m \geq 69.5\text{.}$

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(c)

What if the sampled group was women?

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