Using the slope concept, it is found that the balloon's vertical distance above the ground is of 437.4 feet.
<h3>What is a slope?</h3>
The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.
In this problem:
- The vertical change is x.
- The horizontal change is of 602 ft.
Hence, applying the concept:
tan (36º) = x/602
x = 602 x tan(36º)
x = 437.4.
More can be learned about the slope concept at brainly.com/question/18090623
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Part a)
The simple random sample of size n=36 is obtained from a population with
![\mu = 74](https://tex.z-dn.net/?f=%20%5Cmu%20%3D%2074)
and
![\sigma = 6](https://tex.z-dn.net/?f=%20%5Csigma%20%3D%206)
The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of
![\mu = 74](https://tex.z-dn.net/?f=%20%5Cmu%20%3D%2074)
The standard error of the means becomes the standard deviation of the sampling distribution.
![\sigma_ { \bar X } = \frac{ \sigma}{ \sqrt{n} } \\ \sigma_ { \bar X } = \frac{ 6}{ \sqrt{36} } = 1](https://tex.z-dn.net/?f=%20%5Csigma_%20%7B%20%5Cbar%20X%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csigma%7D%7B%20%5Csqrt%7Bn%7D%20%7D%20%20%5C%5C%20%5Csigma_%20%7B%20%5Cbar%20X%20%7D%20%20%3D%20%20%5Cfrac%7B%206%7D%7B%20%5Csqrt%7B36%7D%20%7D%20%20%3D%201)
Part b) We want to find
![P(\bar X \:>\:75.9)](https://tex.z-dn.net/?f=P%28%5Cbar%20X%20%5C%3A%3E%5C%3A75.9%29%20)
We need to convert to z-score.
![P(\bar X \:>\:75.9) = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: 1.9) \\ = 0.0287](https://tex.z-dn.net/?f=P%28%5Cbar%20X%20%5C%3A%3E%5C%3A75.9%29%20%20%3D%20P%28z%20%5C%3A%3E%5C%3A%20%5Cfrac%7B75.9%20-%2074%7D%7B1%7D%20%29%20%20%5C%5C%20%20%3D%20P%28z%20%5C%3A%3E%5C%3A%20%5Cfrac%7B75.9%20-%2074%7D%7B1%7D%20%29%20%5C%5C%20%20%3D%20P%28z%20%5C%3A%3E%5C%3A%201.9%29%20%5C%5C%20%20%3D%200.0287)
Part c)
We want to find
![P(\bar X \: < \:71.95)](https://tex.z-dn.net/?f=P%28%5Cbar%20X%20%5C%3A%20%3C%20%5C%3A71.95%29%20)
We convert to z-score and use the normal distribution table to find the corresponding area.
![P(\bar X \: < \:71.95) = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: - 2.05) \\ = 0.0202](https://tex.z-dn.net/?f=P%28%5Cbar%20X%20%5C%3A%20%3C%20%5C%3A71.95%29%20%20%3D%20P%28z%20%5C%3A%20%3C%20%5C%3A%20%5Cfrac%7B71.9%205-%2074%7D%7B1%7D%20%29%20%20%5C%5C%20%20%3D%20P%28z%20%5C%3A%20%3C%20%5C%3A%20%5Cfrac%7B71.9%205-%2074%7D%7B1%7D%20%29%20%5C%5C%20%20%3D%20P%28z%20%5C%3A%20%3C%20%5C%3A%20%20-%202.05%29%20%5C%5C%20%20%3D%200.0202)
Part d)
We want to find :
![P(73\:](https://tex.z-dn.net/?f=P%2873%5C%3A%3C%5Cbar%20X%20%3C%5C%3A%2075.75%29)
We convert to z-scores and again use the standard normal distribution table.
![P( \frac{73 - 74}{1} \:< \: z](https://tex.z-dn.net/?f=P%28%20%5Cfrac%7B73%20-%2074%7D%7B1%7D%20%5C%3A%3C%20%5C%3A%20z%20%3C%5C%3A%20%20%5Cfrac%7B75.75%20-%2074%7D%7B1%7D%20%29%20%20%5C%5C%20%3D%20P%28%20%20-%201%5C%3A%3C%20%5C%3A%20z%20%3C%5C%3A%201.75%20%29%20%5C%5C%20%20%3D%200.8013)
Answer:
It would be 66
Step-by-step explanation:
This is how you would graph it
hope this helps :3
the image is below by the way X3
linear function; growth factor of 4