Answer:
(a) 3.75
(b) 2.00083
(c) 0.4898
Step-by-step explanation:
It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].
(a)
Compute the mean of X as follows:
![\mu_{X}=\frac{a+b}{2}=\frac{1.3+6.2}{2}=3.75](https://tex.z-dn.net/?f=%5Cmu_%7BX%7D%3D%5Cfrac%7Ba%2Bb%7D%7B2%7D%3D%5Cfrac%7B1.3%2B6.2%7D%7B2%7D%3D3.75)
(b)
Compute the variance of X as follows:
![\sigm^{2}_{X}=\frac{(b-a)^{2}}{12}=\frac{(6.2-1.3)^{2}}{12}=2.00083](https://tex.z-dn.net/?f=%5Csigm%5E%7B2%7D_%7BX%7D%3D%5Cfrac%7B%28b-a%29%5E%7B2%7D%7D%7B12%7D%3D%5Cfrac%7B%286.2-1.3%29%5E%7B2%7D%7D%7B12%7D%3D2.00083)
(c)
Compute the value of P(X < 3.7) as follows:
![P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898](https://tex.z-dn.net/?f=P%28X%20%3C%203.7%29%3D%5Cint%5Climits%5E%7B3.7%7D_%7B1.3%7D%7B%5Cfrac%7B1%7D%7B6.2-1.3%7D%7D%5C%2C%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4.9%7D%5Ctimes%20%5Bx%5D%5E%7B3.7%7D_%7B1.3%7D%5C%5C%5C%5C%3D%5Cfrac%7B3.7-1.3%7D%7B4.9%7D%5C%5C%5C%5C%5Capprox%200.4898)
Thus, the value of P(X < 3.7) is 0.4898.
Answer:
5 but its probaly not right bc im just looking for pointsStep-by-step explanation:
Answer:
x> 13
Step-by-step explanation:
x-4 >9
Add 4 to each side
x-4+4 >9+4
x> 13
1183 rounded to the nearest hundred = 1200
1145 rounded to the nearest hundred = 1100
C. 4.45 cm. you take the circumference and divide it by pi to find the diameter