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Tom [10]
3 years ago
8

A rectangle has a length of 10 inches and a width of 8 inches

Mathematics
1 answer:
Serjik [45]3 years ago
3 0
I’m assuming you want to work out the area
area = length x width
area = 10 x 8
area = 80 inches^2
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Step-by-step explanation:

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A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w
sergejj [24]

Answer:

a) a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

b) P(X \geq 3) = 1-P(X

c) P(\bar X \geq 225)=1- P(\bar X

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".  

2) Part a

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

X \sim N(225,16.5)  

Where \mu=225 and \sigma=16.5

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=\frac{a-225}{16.5}

And if we solve for a we got

a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

X\sim Bin(n=10, p=0.25)

And we want this probability:

P(X \geq 3) = 1-P(X

We can find the individual probabilities like this:

P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563

P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877

P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816

P(X \geq 3) = 1-P(X

Part c

For this case we know that the distribution for the sample mean is given by:

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

And we want this probability:

P(\bar X \geq 225)

And for this case we can use the complement rule and the z score given by:

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

And if we replace we got:

P(\bar X \geq 225)=1- P(\bar X

4 0
3 years ago
12.5% of a number is 25, find the number
tankabanditka [31]

Answer:

200

Step-by-step explanation:

Let's call the number x :
12.5% of x = 25

Changing 12.5% into decimal would be 0.125

Now we have the equation :

0.125x = 25

Divide both sides by 0.125 to make x the subject :

x = 25 ÷ 0.125

x = 200

To check we can substitute this value into the question :

12.5% of 200 = 25

Hope this helped and have a good day

4 0
1 year ago
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