You have to draw a corrdinate plane to figure it out. then connect the units
Answer:
161 + 162 + 163 = 486
Step-by-step explanation:
(X) + (X + 1) + (X + 2) = 486
X + X + 1 + X + 2 = 486
3X + 3 = 486
3X + 3 - 3 = 486 - 3
3X = 483
3X/3 = 483/3
X = 161
Answer:
(a) The standard deviation of your waiting time is 4.33 minutes.
(b) The probability that you will have to wait more than 2 standard deviations is 0.4227.
Step-by-step explanation:
Let <em>X</em> = the waiting time for the bus at the parking lot.
The random variable <em>X</em> is uniformly distributed with parameters <em>a</em> = 0 to <em>b</em> = 15.
The probability density function of <em>X</em> is given as follows:
![f_{X}(x)=\frac{1}{b-a};\ a](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cfrac%7B1%7D%7Bb-a%7D%3B%5C%20a%3CX%3Cb%2C%5C%20a%3Cb)
(a)
The standard deviation of a Uniformly distributed random variable is given by:
![SD=\sqrt{\frac{(b-a)^{2}}{12}}](https://tex.z-dn.net/?f=SD%3D%5Csqrt%7B%5Cfrac%7B%28b-a%29%5E%7B2%7D%7D%7B12%7D%7D)
Compute the standard deviation of the random variable <em>X</em> as follows:
![SD=\sqrt{\frac{(b-a)^{2}}{12}}](https://tex.z-dn.net/?f=SD%3D%5Csqrt%7B%5Cfrac%7B%28b-a%29%5E%7B2%7D%7D%7B12%7D%7D)
![=\sqrt{\frac{(15-0)^{2}}{12}}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B%2815-0%29%5E%7B2%7D%7D%7B12%7D%7D)
![=\sqrt{\frac{225}{12}}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B225%7D%7B12%7D%7D)
![=\sqrt{18.75}\\=4.33](https://tex.z-dn.net/?f=%3D%5Csqrt%7B18.75%7D%5C%5C%3D4.33)
Thus, the standard deviation of your waiting time is 4.33 minutes.
(b)
The value representing 2 standard deviations is:
![X=2\times SD=2\times4.33=8.66](https://tex.z-dn.net/?f=X%3D2%5Ctimes%20SD%3D2%5Ctimes4.33%3D8.66)
Compute the value of P (X > 8.66) as follows:
![P(X>8.66)=\int\limits^{10}_{8.66} {\frac{1}{15-0}}\, dx\\](https://tex.z-dn.net/?f=P%28X%3E8.66%29%3D%5Cint%5Climits%5E%7B10%7D_%7B8.66%7D%20%7B%5Cfrac%7B1%7D%7B15-0%7D%7D%5C%2C%20dx%5C%5C)
![=\frac{1}{15}\times \int\limits^{10}_{8.66} {1}\, dx\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B15%7D%5Ctimes%20%5Cint%5Climits%5E%7B10%7D_%7B8.66%7D%20%7B1%7D%5C%2C%20dx%5C%5C)
![=\frac{1}{15}\times |x|^{15}_{8.66}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B15%7D%5Ctimes%20%7Cx%7C%5E%7B15%7D_%7B8.66%7D%5C%5C)
![=\frac{15-8.66}{15}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B15-8.66%7D%7B15%7D%5C%5C)
![=0.4227](https://tex.z-dn.net/?f=%3D0.4227)
Thus, the probability that you will have to wait more than 2 standard deviations is 0.4227.
Answer:
77°
Step-by-step explanation:
Angles on a straight line add up to 180
180 - 103 = b
180 - 103 = 77
It should be 3 do you understand?