The first is the correct
Δ ZYB ≈ Δ OWR by SSS
because:
ZB = OR = 5
ZY = OW = 3
YB = WR = 5.5
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
a) For x < 2:
![z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B2-7%7D%7B2.4%7D%20%3D-2.08)
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
![z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B2-7%7D%7B2.4%7D%20%3D-2.08)
For x = 11:
![z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B11-7%7D%7B2.4%7D%20%3D1.67)
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
![z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B11-7%7D%7B2.4%7D%20%3D1.67)
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
![z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B2-7%7D%7B2.4%7D%20%3D-2.08)
For x = 5:
![z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B5-7%7D%7B2.4%7D%20%3D-0.83)
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
![z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B5-7%7D%7B2.4%7D%20%3D-0.83)
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
Find the slope of the line first:
5x - 2y = -6,
y = (5/2)x + 3;
Since we need a line that's perpendicular, m = - (2/5).
The only equation that has the slope of this m is 2x + 5y = -10;