Answer:
There is not even a question what shall I answer
Step-by-step explanation:
Answer choice 2
this is because the center is at 2,-3 and radius is 5, 5^2 = 25
100 = x^2 + y^2
So
2 x dx/dt + 2y dy/dt =0
So
dy/dt = -x/y dx/dt
= -x/sqrt(100-x^2) * 7 At x=3
Answer:
![P(\bar X >70)= P(Z>\frac{70-69}{\frac{4}{\sqrt{36}}})= P(Z>1.5)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29%3D%20P%28Z%3E%5Cfrac%7B70-69%7D%7B%5Cfrac%7B4%7D%7B%5Csqrt%7B36%7D%7D%7D%29%3D%20P%28Z%3E1.5%29)
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
![P(Z>1.5)=1-P(Z,1.5) = 1-0.933=0.0668](https://tex.z-dn.net/?f=%20P%28Z%3E1.5%29%3D1-P%28Z%2C1.5%29%20%3D%201-0.933%3D0.0668)
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:
Where
and
And we select a sample size of n =70
From the central limit theorem (n>30)we know that the distribution for the sample mean
is given by:
And we want to find this probability:
![P(\bar X >70)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29)
And we can use the z score formula given by:
![z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And using this formula we got:
![P(\bar X >70)= P(Z>\frac{70-69}{\frac{4}{\sqrt{36}}})= P(Z>1.5)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29%3D%20P%28Z%3E%5Cfrac%7B70-69%7D%7B%5Cfrac%7B4%7D%7B%5Csqrt%7B36%7D%7D%7D%29%3D%20P%28Z%3E1.5%29)
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
![P(Z>1.5)=1-P(Z,1.5) = 1-0.933=0.0668](https://tex.z-dn.net/?f=%20P%28Z%3E1.5%29%3D1-P%28Z%2C1.5%29%20%3D%201-0.933%3D0.0668)