Olivia used 1/2 pound of peppers and 1/15 pound of cheese to make three pizzas. If she uses the same recipe to make five pizzas how much cheese is needed?

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Ayallaric6875

10.01.2023

Mathematics

$\mathbb P(X\le104)=\mathbb P\left(\dfrac{X-98}6\le\dfrac{104-98}6\right)=\mathbb P(Z\le1)$

The empirical rule states that approximately 68% of a normal distribution falls within one standard deviation of the mean, or $\mathbb P(-1\le Z\le1)\approx0.68$ . This means, by symmetry of the distribution, that $\mathbb P(0\le Z\le1)\approx0.5\times0.68=0.34$

Now, since the distribution is symmetric about the mean, you have $\mathbb P(Z\le0)=0.5$ .

So,

$\mathbb P(Z\le1)=\mathbb P(Z\le0)+\mathbb P(0\le Z\le 1)\approx0.5+0.34=0.84$

More precisely, this probability is around 0.841345

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Olivia used 1/2 pound of peppers and 1/15 pound of cheese to make three pizzas. If she uses the same recipe to make five pizzas how much cheese is needed?￼