Answer:
$521.58 < μ < $666.1
Step-by-step explanation:
Spring break can be a very expensive holiday. A sample of 80 students is surveyed, and the average amount spent by students on travel and beverages is $593.84 at 92% confidence level. The sample standard deviation is approximately $369.34. Is $521.58 ≤μ≤ $666.10 correct?
Given that:
number of samples (n) = 80 students, mean (μ) = $593.84, standard deviation (σ) = $369.34, confidence level (c) = 92% = 0.92.
α = 1 - c = 1 - 0.92 = 0.08
![\frac{\alpha }{2} =\frac{0.08}{2} = 0.04](https://tex.z-dn.net/?f=%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%3D%5Cfrac%7B0.08%7D%7B2%7D%20%3D%200.04)
the z score of 0.46 (0.5 - 0.04) is the same as the z score of 0.04. This is gotten from the Normal Distribution Table.
Therefore, ![z_{\frac{\alpha }{2} }=z_{0.04}=1.75](https://tex.z-dn.net/?f=z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%3Dz_%7B0.04%7D%3D1.75)
The margin of error (e) is given as:
![e=z_{0.04}\frac{\sigma}{\sqrt{n} }=1.75*\frac{369.34}{\sqrt{80} } =72.26](https://tex.z-dn.net/?f=e%3Dz_%7B0.04%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%3D1.75%2A%5Cfrac%7B369.34%7D%7B%5Csqrt%7B80%7D%20%7D%20%20%3D72.26)
The confidence interval = (μ - e, μ + e) = ($593.84 - $72.26, $593.84 + $72.26) = ($521.58, $666.1)
The confidence interval is $521.58 < μ < $666.1
Answer:
14.5 units
Step-by-step explanation:
we need to find the length of the rectangle. To do that, we must find the hypotenuse of the right triangle below the rectangle.
Finding the hypotenuse of a right triangle uses the Pythagorean theorem, or a² + b² = c²
let a be 9 and b be 7.
9² + 7² = c²
81 + 49 = c²
130 = c²
√130 = c
c = approx. 11.4
Now, we know the length of the rectangle.
Once a rectangle is cut diagonally, it forms 2 equal right triangles. We will use the same process to find the hypotenuse of the second right triangle.
9² + 11.4² = c²
81 + 130 = c²
81 + 130 = approx. 211
c² = 211
√211 = c
c = approx. 14.5
Answer:
c = 9
Step-by-step explanation:
Answer:
Two lines intersect at right angles. Conclusion: The two lines are
perpendicular.
Step-by-step explanation:
Answer:
34.56 inches
Step-by-step explanation:
The formula for the circumference is : ![\pi *diameter](https://tex.z-dn.net/?f=%5Cpi%20%2Adiameter)
The diameter is the full length of the interior of a circle.
To work this out you would simply multiply the diameter of 11 by pi, which gives you 34.56.
1) Multiply pi by 11.
![\pi *11=34.56](https://tex.z-dn.net/?f=%5Cpi%20%2A11%3D34.56)