The question is incomplete. Here is the complete question.
Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes
a) 3 minutes or less
b) 4 minutes of less
c) 5 minutes of less
d) Longer than 5 minutes
e) Longer than 7 minutes
Answer: a) P(X<3) = 0.882
b) P(X<4) = 0.908
c) P(X<5) = 0.928
d) P(X>5) = 0.286
e) P(X>7) = 0.174
Step-by-step explanation: <u>Exponential</u> <u>distribution</u> is related with teh amount of time until some specific event happens.
If X is a continuous random variable, probability is calculated as:
![P(X](https://tex.z-dn.net/?f=P%28X%3Cx%29%20%3D%201-me%5E%7B-mx%7D)
in which:
m is decay parameter, given by: ![m=\frac{1}{mean}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7Bmean%7D)
For the Nite Time Inn calls:
![m=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B4%7D)
m = 0.25
(a) P(X<3)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25e%5E%7B-0.25.3%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25e%5E%7B-0.75%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25%2A0.472)
P(X < 3) = 0.882
<u>The probability the call takes less than 3 minutes is 0.882.</u>
(b) P(X<4)
![P(X](https://tex.z-dn.net/?f=P%28X%3C4%29%20%3D%201-0.25e%5E%7B-0.25.4%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C4%29%20%3D%201-0.25e%5E%7B-1%7D)
P(X < 4) = 0.908
<u>The probability the call takes less tahn 4 minutes is 0.908.</u>
(c) P(X<5)
![P(X](https://tex.z-dn.net/?f=P%28X%3C5%29%20%3D%201-0.25e%5E%7B-0.25.5%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C5%29%20%3D%201-0.25e%5E%7B-1.25%7D)
P(X < 5) = 0.928
<u>The probability of calls taking less than 5 minutes is 0.928.</u>
(d) P(X>5)
Knowing that the sum of probabilities of less than and more than has to equal 1:
P(X<x) + P(X>x) = 1
P(X>x) = 1 - P(PX<x)
![P(X>x) = 1-(1-me^{-m*x})](https://tex.z-dn.net/?f=P%28X%3Ex%29%20%3D%201-%281-me%5E%7B-m%2Ax%7D%29)
![P(X>x)=me^{-mx}](https://tex.z-dn.net/?f=P%28X%3Ex%29%3Dme%5E%7B-mx%7D)
For P(X>5):
![P(X>5) = 0.25e^{-1.25}](https://tex.z-dn.net/?f=P%28X%3E5%29%20%3D%200.25e%5E%7B-1.25%7D)
P(X > 5) = 0.286
<u>The probability of calls taking more than 5 minutes is 0.286.</u>
(e) P(X>7)
![P(X>7)=0.25e^{-0.25.7}](https://tex.z-dn.net/?f=P%28X%3E7%29%3D0.25e%5E%7B-0.25.7%7D)
![P(X>7)=0.25e^{-1.75}](https://tex.z-dn.net/?f=P%28X%3E7%29%3D0.25e%5E%7B-1.75%7D)
P(X > 7) = 0.174
<u>The probability of calls taking more than 7 minutes is 0.174.</u>
As you get older your brain develops as you do so when you’re taught math your brain is developing a slightly slower pace than it should be for example if you have a teacher who doesn’t really teach a lot it’s really going to slow down the process of learning
Well any number you add can be irrational need more information.
Answer:
B. It is isometric because all side lengths and angle measures remained the same
Step-by-step explanation:
So you know the school donated 9 pies, so you want to know how many pieces are in 9 pies. (remember 8 pieces per 1 pie)
9 x 8 = 72
Next you subtract the amount you got to total amount.(224)
So 224 - 72 is 152.
152 is how many pieces of pie were sold by students.
To configure this number back to amount of pie, you basically need to divide by 8(number of pieces in 1 pie).
152 divided by 8 is 19. So 19 pies were sold by students.
Hope this helped!