Answer:
Top 3%: 4.934 cm
Bottom 3%: 4.746 cm
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 4.84, \sigma = 0.05](https://tex.z-dn.net/?f=%5Cmu%20%3D%204.84%2C%20%5Csigma%20%3D%200.05)
Top 3%
Value of Z when Z has a pvalue of 1 - 0.03 = 0.97. So X when Z = 1.88.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![1.88 = \frac{X - 4.84}{0.05}](https://tex.z-dn.net/?f=1.88%20%3D%20%5Cfrac%7BX%20-%204.84%7D%7B0.05%7D)
![X - 4.84 = 0.05*1.88](https://tex.z-dn.net/?f=X%20-%204.84%20%3D%200.05%2A1.88)
![X = 4.934](https://tex.z-dn.net/?f=X%20%3D%204.934)
Bottom 3%
Value of Z when Z has a pvalue of 0.03. So X when Z = -1.88.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.88 = \frac{X - 4.84}{0.05}](https://tex.z-dn.net/?f=-1.88%20%3D%20%5Cfrac%7BX%20-%204.84%7D%7B0.05%7D)
![X - 4.84 = 0.05*(-1.88)](https://tex.z-dn.net/?f=X%20-%204.84%20%3D%200.05%2A%28-1.88%29)
![X = 4.746](https://tex.z-dn.net/?f=X%20%3D%204.746)
The total cost of ordering 10 shirts can be calculated as following:
C = 4 + 12(10)
C = 4 + 120
C = 124
Answer:
x=pi*n/2+1/2arctan(7/5)
Step-by-step explanation:
5sin(2x)=7cos(2x)
5tan(2x)=7/5
2x=pi*n+arctan(7/5)
x=pi*n/2+1/2arctan(7/5) for n e Z
Answer:
Diameter of sphere = 18 cm
Step-by-step explanation:
<h2>Volume of Cylinder and Sphere:</h2><h3> Cylinder:</h3>
Diameter = 18 cm
r = 18÷ 2 = 9 cm
h = 12 cm
![\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}](https://tex.z-dn.net/?f=%5Csf%20%5Cboxed%7B%5Cbf%20Volume%20%5C%20of%20%5C%20cylinder%20%3D%20%5Cpi%20r%5E2h%7D)
= π * 9 * 9 * 12 cm³
<h3>Sphere:</h3>
![\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}](https://tex.z-dn.net/?f=%5Csf%20%5Cboxed%7B%5Ctext%7B%5Cbf%20Volume%20of%20sphere%20%3D%20%24%5Cdfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3%24%7D%7D)
Solid cylinder is melted and turned into a solid sphere.
Volume of sphere = volume of cylinder
![\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%20%3D%20%5Cpi%20%2A9%2A9%2A12)
![\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}](https://tex.z-dn.net/?f=%5Csf%20r%5E%7B3%7D%3D%20%5Cdfrac%7B%5Cpi%20%2A9%2A9%2A12%2A3%7D%7B4%2A%5Cpi%20%7D%5C%5C%5C%5C%20%20r%5E%7B3%7D%3D9%20%2A%209%20%2A3%20%2A3%5C%5C%5C%5C%5C%5Cr%20%3D%20%5Csqrt%5B3%5D%7B9%2A9%2A9%7D%5C%5C%5C%5C%20r%20%3D%209%20%5C%20cm%5C%5C%5C%5Cdiameter%20%3D%209%2A2%5C%5C%5C%5C%5Cboxed%7Bdiameter%20%5C%20of%20%5C%20%20sphere%20%3D%2018%20%5C%20cm%7D)
How would be so that. Where is the graph