A.
![\mathbb P(X>1000)=\mathbb P\left(\dfrac{X-1200}{100}>\dfrac{1000-1200}{100}\right)=\mathbb P(Z>-2)](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3E1000%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-1200%7D%7B100%7D%3E%5Cdfrac%7B1000-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28Z%3E-2%29)
Since about 95% of a normal distribution falls within two standard deviations of the mean, that leaves 5% that lie without, with 2.5% lying to either side.
![\mathbb P(Z>-2)=\mathbb P(|Z|2)=0.95+0.025=0.975](https://tex.z-dn.net/?f=%5Cmathbb%20P%28Z%3E-2%29%3D%5Cmathbb%20P%28%7CZ%7C%3C2%29%2B%5Cmathbb%20P%28Z%3E2%29%3D0.95%2B0.025%3D0.975)
b.
![\mathbb P(1100](https://tex.z-dn.net/?f=%5Cmathbb%20P%281100%3CX%3C1300%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7B1100-1200%7D%7B100%7D%3C%5Cdfrac%7BX-1200%7D%7B100%7D%3C%5Cdfrac%7B1300-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28-1%3CZ%3C1%29)
About 68% of a normal distribution lies within one standard deviation of the mean, so this probability is about 0.68.
c. You're looking for
![k](https://tex.z-dn.net/?f=k)
such that
![\mathbb P(X>k)=0.10](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3Ek%29%3D0.10)
Since
![\mathbb P(X>k)=\mathbb P\left(\dfrac{X-1200}{100}>\dfrac{k-1200}{100}\right)=\mathbb P(Z>k^*)=0.10](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3Ek%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-1200%7D%7B100%7D%3E%5Cdfrac%7Bk-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28Z%3Ek%5E%2A%29%3D0.10)
occurs for
![k^*\approx1.2816](https://tex.z-dn.net/?f=k%5E%2A%5Capprox1.2816)
, it follows that
![\dfrac{k-1200}{100}=1.2816\implies k\approx1328](https://tex.z-dn.net/?f=%5Cdfrac%7Bk-1200%7D%7B100%7D%3D1.2816%5Cimplies%20k%5Capprox1328)
So there's a probability of 0.10 for having a demand exceeding about 1328 pounds.
Answer:
all of them (A, B, C, D)
Step-by-step explanation:
Two unique points define a line. Any pair of unique points will always be collinear (reside on the same line).
Each of the points listed, together with (2, 1), will define a line. The two points will be collinear.
Answer: look at my work its 10 pi cm ^2
Step-by-step explanation:
Answer:
Since we are talking annual interest and, I assume a time period of 1 year:
The interest earned is the sum of the interest earned on the two loans separately
Let x = amount loaned at 14%
18,500-x = amount loaned at 12%
I = prt
p = x and 18500-x
r = 0.14 and 0.12
t = 1
2390 = 0.14x + 0.1(18500-x)
2390 = .14x + 1850 - 0.1x
x = 13500
x = $13,500 loaned at 14%
18500-x = $5,000 loaned at 12%
Answer:
7.5 feet
Step-by-step explanation:
4/5=6/x
cross multiply
4x=30
x=7.5