2rd one I could be wrong tho
We have been given for a normal distribution the mean time it takes to walk to the bus stop is 8 minutes with a standard deviation of 2 minutes. And the mean time it takes for the bus to get to school is 20 minutes with a standard deviation of 4 minutes.
(a) Average time that it would take reach school can be obtained by adding the average times.
8+20 = 28 minutes.
(b) Standard deviation of the trip to school can be found as:
![\sigma =\sqrt{2^{2}+4^{2}}=\sqrt{4+16}=\sqrt{20}=4.47](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B2%5E%7B2%7D%2B4%5E%7B2%7D%7D%3D%5Csqrt%7B4%2B16%7D%3D%5Csqrt%7B20%7D%3D4.47)
Therefore, standard deviation of the entire trip is 4.47 minutes.
(c) Let us first find z score corresponding to 30 minutes.![z=\frac{x-\mu }{\sigma }=\frac{30-28}{4.47}=0.447](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%20%7D%7B%5Csigma%20%7D%3D%5Cfrac%7B30-28%7D%7B4.47%7D%3D0.447)
We need to find the probability such that ![P(x>30)=P(z>0.447)=0.67](https://tex.z-dn.net/?f=P%28x%3E30%29%3DP%28z%3E0.447%29%3D0.67)
Therefore, the required probability is 0.67.
(d) If average time to walk to school is 10 minutes, then overall average time for the trip will be 10+20 = 30 minutes.
(e) Standard deviation won't change it will remain 4.47
(f) The new probability will be:
![z=\frac{x-\mu }{\sigma }=\frac{30-90}{4.47}=0](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%20%7D%7B%5Csigma%20%7D%3D%5Cfrac%7B30-90%7D%7B4.47%7D%3D0)
![P(x>30)=P(z>0)=0.5](https://tex.z-dn.net/?f=P%28x%3E30%29%3DP%28z%3E0%29%3D0.5)
Therefore, probability will be 0.50.
Answer:
The length of rectangle is 6 units and the width is 1.5 units
Step-by-step explanation:
Let
L -----> the length of rectangle
W ----> the width of rectangle
we know that
The area of rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
we have
![A=9\ units^{2}](https://tex.z-dn.net/?f=A%3D9%5C%20units%5E%7B2%7D)
so
-----> equation A
A rectangle width is one fourth it’s length
so
----> equation B
substitute equation B in equation A and solve for L
![L^{2}=9*4](https://tex.z-dn.net/?f=L%5E%7B2%7D%3D9%2A4)
![L^{2}=36](https://tex.z-dn.net/?f=L%5E%7B2%7D%3D36)
take square root both sides
![L=6\ units](https://tex.z-dn.net/?f=L%3D6%5C%20units)
Find the value of W
![W=\frac{1}{4}(6)](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1%7D%7B4%7D%286%29)
![W=1.5\ units](https://tex.z-dn.net/?f=W%3D1.5%5C%20units)
Answer:
6/x^4
Step-by-step explanation: