Answer:
The probability is 0.953
Step-by-step explanation:
We know that the mean
is:
![\mu=10:30\ p.m](https://tex.z-dn.net/?f=%5Cmu%3D10%3A30%5C%20p.m)
The standard deviation
is:
![\sigma=0:15\ minutes](https://tex.z-dn.net/?f=%5Csigma%3D0%3A15%5C%20minutes)
The Z-score is:
![Z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
We seek to find
![P(10:00\ p.m.](https://tex.z-dn.net/?f=P%2810%3A00%5C%20p.m.%3Cx%3C11%3A00%5C%20p.m.%29)
The Z-score is:
![Z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![Z=\frac{10:00-10:30}{0:15}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B10%3A00-10%3A30%7D%7B0%3A15%7D)
![Z=\frac{-0:30}{0:15}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B-0%3A30%7D%7B0%3A15%7D)
![Z=-2](https://tex.z-dn.net/?f=Z%3D-2)
The score of Z =-2 means that 10:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%
and
![Z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![Z=\frac{11:00-10:30}{0:15}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B11%3A00-10%3A30%7D%7B0%3A15%7D)
![Z=\frac{0:30}{0:15}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B0%3A30%7D%7B0%3A15%7D)
![Z=2](https://tex.z-dn.net/?f=Z%3D2)
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%
![P(10:00\ p.m.](https://tex.z-dn.net/?f=P%2810%3A00%5C%20p.m.%3Cx%3C11%3A00%5C%20p.m.%29%3D100%5C%25-2.35%5C%25-2.35%5C%25)
![P(10:00\ p.m.](https://tex.z-dn.net/?f=P%2810%3A00%5C%20p.m.%3Cx%3C11%3A00%5C%20p.m.%29%3D95.3%5C%25)
![P(10:00\ p.m.](https://tex.z-dn.net/?f=P%2810%3A00%5C%20p.m.%3Cx%3C11%3A00%5C%20p.m.%29%3D0.953)
Answer:
(a) Average number of cars in the system is 1
(b) Average time a car waits is 12 minutes
(c) Average time a car spends in the system is 2 minutes
(d) Probability that an arrival has to wait for service is 0.08.
Step-by-step explanation:
We are given the following
Arrival Rate, A = 2.5
Service Rate B = 5
(a) Average Number of Cars in the System is determined by dividing the Arrival Rate A by the difference between the Service Rate B, and Arrival Rate A.
Average number of cars = A/(B - A)
= 2.5/(5 - 2.5)
= 2.5/2.5 = 1
There is an average of 1 car.
(b) Average time a car waits = A/B(B - A)
= 2.5/5(5 - 2.5)
= 2.5/(5 × 2.5)
= 2.5/12.5
= 1/5
= 0.20 hours
Which is 12 minutes
(c) Average time a car spends in the system is the ratio of the average time a car waits to the service rate.
Average time = 0.2/5
= 0.04 hours
= 2.4 minutes
Which is approximately 2 minutes.
(d) Probability that an arrival has to wait for service is the ratio of the average time a car waits to rate of arrivals.
Probability = 0.2/2.5
= 0.08
Because Meg gets an additional 6 ponies, she adds them to her existing 26 ponies. This makes her have 32 ponies.
(CHECK: 26+6=32, 32-6=26)
Since she displays half of her 32, that means 16 of her ponies are on display.
(CHECK: 32/2=16, 16+16=32)
Hopefully this helps!! :)
Answer:
B. The second choice.
Step-by-step explanation:
A function cannot have two points with the same x-coordinate.
If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.
Answer:
0
Step-by-step explanation:
0 is the identity element under addition for the real numbers.