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damaskus [11]
4 years ago
5

There are 4 different mathematics books and 5 different science books.In how many ways can the books be arrange on a shelf if th

ere are no restrictions
Mathematics
1 answer:
Vedmedyk [2.9K]4 years ago
3 0

Answer:

9!=362880 ways

Step-by-step explanation:

It is given that there are 4 different mathematics books and 5 different science books.

So basically there are 9 different books. So we have 9 choices for the first book, 8 choices for the second book, since we have placed the first one. We have 7 choices for the third book and so on. Therefore, we can arrange 9 different books in,

!9 ways, on solving !9 we get,

!9= 9 \times 8 \times 7 \times 6 ....\times 1= 362880

So there are 362,880 ways to arrange 9 different books if there are no restrictions.

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The weights of ice cream cartons are normally distributed with a mean weight of 1313 ounces and a standard deviation of 0.50.5 o
asambeis [7]

Answer:

a) We are interested on this probability

P(X>13.17)

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>13.17)=P(\frac{X-\mu}{\sigma}>\frac{13.17-\mu}{\sigma})=P(Z>\frac{13.17-13}{0.5})=P(z>0.34)=0.367

b) P(\bar X >13.17)

The new z score is given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

P(\bar X >13.17)=P(Z> \frac{13.17-13}{\frac{0.5}{\sqrt{36}}})= P(Z>2.04) =0.0207

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".  

Part a

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

X \sim N(13,0.5)  

Where \mu=13 and \sigma=0.5

We are interested on this probability

P(X>13.17)

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>13.17)=P(\frac{X-\mu}{\sigma}>\frac{13.17-\mu}{\sigma})=P(Z>\frac{13.17-13}{0.5})=P(z>0.34)=0.367

Part b

Since the distribution for X is normal then we can conclude that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we want this probability:

P(\bar X >13.17)

The new z score is given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

P(\bar X >13.17)=P(Z> \frac{13.17-13}{\frac{0.5}{\sqrt{36}}})= P(Z>2.04) =0.0207

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Step-by-step explanation:

I hope this helps you out!

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Answer:

Step-by-step explanation:

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