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Scilla [17]
3 years ago
5

jess wants to make cupcakes. To make cupcakes, she needs 3 1/4 cups of flour per batch of cupcakes. If Jess has 57 cups of flour

, then how many batches of cupcakes can she make?
Mathematics
2 answers:
inysia [295]3 years ago
7 0
To solve this, we have to divide 57 cups (the total amount she has) by 3.25 (the amount she needs per batch). When we do this, we get 17. 54, but we'll round down because Jess can't make 0.54 of a batch of cupcakes.
Your answer should be 17 batches. I hope this helps!
lawyer [7]3 years ago
4 0
5 is the most amount of batches jess can make with 57 cups of flour
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Answer:

a) P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

b) P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

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c) z=0.674

And if we solve for a we got

a=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(43,4.5)  

Where \mu=43 and \sigma=4.5

Part a

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard distribution or excel and we got:

P(z

Part b

P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

P(z>3.78)=1-P(Z

Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=43 +0.674*4.5=46.033

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.  

8 0
3 years ago
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