Susan made $117 for hours 9 of work.

1 answer:

8 0

First we need to figure out how much Susan made per hour

117/9 = 13 dollars per hour

Then find out how much she makes in 7 hours

13 • 7 = 91 dollars

$91 in 7 hours

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How do you find the normal approximation without using the continuity correction?

Dennis_Churaev [7]

Let's say you want to compute the probability $\mathbb P(a\le X\le b)$ where $X$ converges in distribution to $Y$ , and $Y$ follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing $Y$ such that its mean and variance are the same as those for $X$ .

Example: If $X$ is binomially distributed with $n=100$ and $p=0.1$ , then $X$ has mean $np=10$ and variance $np(1-p)=9$ . So you can approximate a probability in terms of $X$ with a probability in terms of $Y$ :

$\mathbb P(a\le X\le b)\approx\mathbb P(a\le Y\le b)=\mathbb P\left(\dfrac{a-10}3\le\dfrac{Y-10}3\le\dfrac{b-10}3\right)=\mathbb P(a^*\le Z\le b^*)$

where $Z$ follows the standard normal distribution.