Answer:
![a. \ P(X=0)=5.574\times10^{-7}](https://tex.z-dn.net/?f=a.%20%5C%20P%28X%3D0%29%3D5.574%5Ctimes10%5E%7B-7%7D)
![b. \ \ P(X\leq 1)=8.584\times10^{-6}](https://tex.z-dn.net/?f=b.%20%5C%20%5C%20P%28X%5Cleq%201%29%3D8.584%5Ctimes10%5E%7B-6%7D)
![c.\ \ \ P(X\geq 4)=0.9997](https://tex.z-dn.net/?f=c.%5C%20%5C%20%5C%20P%28X%5Cgeq%204%29%3D0.9997)
Step-by-step explanation:
a. #We notice this is a Poisson probability function expressed as:
![f(x)=\frac{\mu^xe^{-\mu}}{x!}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D)
x-number of occurrences in a given interval.
-mean occurrences of the event
-The mean is calculated as:
![\mu=\frac{14.4}{4}=3.6](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7B14.4%7D%7B4%7D%3D3.6)
#the probability of no accidents in a 15-minute period is :
![P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X=0)=\frac{14.4^0e^{-14.4}}{0!}\\\\=5.574\times10^{-7}](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D%5C%5C%5C%5CP%28X%3D0%29%3D%5Cfrac%7B14.4%5E0e%5E%7B-14.4%7D%7D%7B0%21%7D%5C%5C%5C%5C%3D5.574%5Ctimes10%5E%7B-7%7D)
Hence, the probability of no accident in a 15-min period is ![=5.574\times10^{-7}](https://tex.z-dn.net/?f=%3D5.574%5Ctimes10%5E%7B-7%7D)
b. The the probability of at least one accident in a 15-minute period. is calculated as:
![P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X\leq 1)=\frac{14.4^0e^{-14.4}}{0!}+\frac{14.4^1e^{-14.4}}{1!}\\\\=5.574\times10^{-7}+8.026\times 10^{-6}\\\\=8.584\times 10^{-6}](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D%5C%5C%5C%5CP%28X%5Cleq%201%29%3D%5Cfrac%7B14.4%5E0e%5E%7B-14.4%7D%7D%7B0%21%7D%2B%5Cfrac%7B14.4%5E1e%5E%7B-14.4%7D%7D%7B1%21%7D%5C%5C%5C%5C%3D5.574%5Ctimes10%5E%7B-7%7D%2B8.026%5Ctimes%2010%5E%7B-6%7D%5C%5C%5C%5C%3D8.584%5Ctimes%2010%5E%7B-6%7D)
Hence, the probability of at least one accident in a 15-minute period is ![8.584\times10^{-6}](https://tex.z-dn.net/?f=8.584%5Ctimes10%5E%7B-6%7D)
c. The probability of four or more accidents in a 15-minute period is calculated as:
![P(X\geq 4)=1-P(X\leq 3)=1-[P(X=0)+P(X1)+P(X=2)+P(X=3)]\\\\=1-[5.574\times10^{-7}+a. \ 8.026\times10^{-6}+\frac{14.4^2e^{-14.4}}{2!}+\frac{14.4^3e^{-14.4}}{3!}]\\\\=1-[8.584\times 10^{-6}+5.779\times10^{-5}+2.774\times10^{-4}]\\\\=0.9997](https://tex.z-dn.net/?f=P%28X%5Cgeq%204%29%3D1-P%28X%5Cleq%203%29%3D1-%5BP%28X%3D0%29%2BP%28X1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%5C%5C%5C%5C%3D1-%5B5.574%5Ctimes10%5E%7B-7%7D%2Ba.%20%5C%208.026%5Ctimes10%5E%7B-6%7D%2B%5Cfrac%7B14.4%5E2e%5E%7B-14.4%7D%7D%7B2%21%7D%2B%5Cfrac%7B14.4%5E3e%5E%7B-14.4%7D%7D%7B3%21%7D%5D%5C%5C%5C%5C%3D1-%5B8.584%5Ctimes%2010%5E%7B-6%7D%2B5.779%5Ctimes10%5E%7B-5%7D%2B2.774%5Ctimes10%5E%7B-4%7D%5D%5C%5C%5C%5C%3D0.9997)
Hence,the probability of four or more accidents in a 15-minute period. is 0.9997
10:21
There are 10 males and males plus females equal 21
Answer : 3.50t + 12
Step - by - step explanation :
the reason why I think the answer is " 3.50t + 12 " is because . . . since the admission to the state farm is only ONCE - there doesn't need to be a variable there to tell us that it MIGHT repeat more than once. and because we don't know how many ride ticket will be purchased - there is a variable there to tell us unknown.
45+15+25=85
100-85=15
Answer: 15% of people prefer neither coffee or juice
Answer: He has a balance of negative 15
Step-by-step explanation:
40 times 4 = 160
135 - 160 = -25
-25 + 100 = 75
30 times 3 = 90
75-90 = -15