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3 years ago

Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies

Mathematics

2 answers:

Leno4ka [110]3 years ago

7 0

Answer: 6

Step-by-step explanation: 8 times 3/4 equals to 6.

zubka84 [21]3 years ago

6 0

Answer:

6 teaspoons

Step-by-step explanation:

Number of teaspoon in 1 batch = 3/4

Number of teaspoon in 8 batches = ?

We know the quantity of teaspoon of vanilla for one batch. To find the quantity for 8 batches we will simply multiply the quantity of teaspoon of vanilla for one batch by 8

=3/4 * 8

=3*2

Therefore 6 teaspoons will be needed....

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Answer:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

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The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We don't have a prior estimation for the proportion $\hat p$ so we can use 0.5 as an approximation for this case

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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Answer:

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