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vlabodo [156]
3 years ago
12

4 questions 20 points

Mathematics
1 answer:
Dvinal [7]3 years ago
3 0
1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7

2.  (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR  3 1/5

3.  (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11

4.  (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
-30 = x


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Answer:

a) P(\bar X

b)P(98

c) P(\bar X

d) P(93

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 heights of a population, and for this case we know the distribution for X is given by:

X \sim N(99.9,30)  

Where \mu=99.9 and \sigma=30

We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:

\bar X \sim N(\mu =99.9 , \frac{\sigma}{\sqrt{n}}= \frac{30}{\sqrt{38}}=4.87)

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

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

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

P(\bar X

=P(Z

Part b

For this case we want this probability:

P(98

=P(\frac{98-99.9}{\frac{30}{\sqrt{38}}}

And we can find this probability on this way:

P(-0.39

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-0.39

Part c

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

P(\bar X

P(\bar X

Part d

For this case we want this probability:

P(93

=P(\frac{93-99.9}{\frac{30}{\sqrt{38}}}

And we can find this probability on this way:

P(-1.42

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-1.42

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3 years ago
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Step-by-step explanation:

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Number( a) shouldn't be zero.

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