Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
![S \sim N ( 1200,60)](https://tex.z-dn.net/?f=S%20%5Csim%20N%20%28%201200%2C60%29)
the probability that the sample mean will be larger than 1224 will now be:
![P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D%20P%28%5Cdfrac%7B%5Coverline%20X%20-%20%5Cmu%20%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%7D%3E%20%5Cdfrac%7B%7D%7B%7D%5Cdfrac%7B1224-%20%5Cmu%20%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%7D%29)
![P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D%20P%28Z%20%3E%20%5Cdfrac%7B1224-%201200%20%7D%7B%5Cdfrac%7B60%7D%7B%5Csqrt%7B36%7D%7D%20%7D%29)
![P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D%20P%28Z%20%3E%20%5Cdfrac%7B24%20%7D%7B%5Cdfrac%7B60%7D%7B6%7D%20%7D%29)
![P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D%20P%28Z%20%3E%20%5Cdfrac%7B24%20%7D%7B10%7D%20%7D%29)
![P(\overline X > 1224) = P(Z > 2.4 })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D%20P%28Z%20%3E%202.4%20%7D%29)
![P(\overline X > 1224) =1 - P(Z \leq 2.4 })](https://tex.z-dn.net/?f=P%28%5Coverline%20X%20%3E%201224%29%20%3D1%20-%20%20P%28Z%20%5Cleq%202.4%20%7D%29)
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
Answer:
x=115⁰
z=27⁰
Step-by-step explanation:
65+x=180 -> Due to same side interior being equal to 180 degrees
<u><em>x= 115</em></u>
x = 3z + 34 -> opposite interior being equal
115 = 3z + 34
81 = 3z
divide by 3 on both sides
<u><em>z=27</em></u>
Answer:
Look at the pics
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask!
Answer:
360 degrees
Step-by-step explanation:
170.02 is a irrational number..has a decimal, cannot be expressed as a fraction.