Answer:
a) P(x=3)=0.089
b) P(x≥3)=0.938
c) 1.5 arrivals
Step-by-step explanation:
Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.
The variable X is modeled by a Poisson process with a rate parameter of λ=6.
The probability of exactly k arrivals in a particular hour can be written as:
a) The probability that exactly 3 arrivals occur during a particular hour is:
b) The probability that <em>at least</em> 3 people arrive during a particular hour is:
![P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938](https://tex.z-dn.net/?f=P%28x%5Cgeq3%29%3D1-%5BP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%5D%5C%5C%5C%5C%5C%5CP%280%29%3D6%5E%7B0%7D%20%5Ccdot%20e%5E%7B-6%7D%2F0%21%3D1%2A0.0025%2F1%3D0.002%5C%5C%5C%5CP%281%29%3D6%5E%7B1%7D%20%5Ccdot%20e%5E%7B-6%7D%2F1%21%3D6%2A0.0025%2F1%3D0.015%5C%5C%5C%5CP%282%29%3D6%5E%7B2%7D%20%5Ccdot%20e%5E%7B-6%7D%2F2%21%3D36%2A0.0025%2F2%3D0.045%5C%5C%5C%5C%5C%5CP%28x%5Cgeq3%29%3D1-%5B0.002%2B0.015%2B0.045%5D%3D1-0.062%3D0.938)
c) In this case, t=0.25, so we recalculate the parameter as:
The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.
Answer: 0.7
Step-by-step explanation:
p(tail) + p(head) = 1
p(tail) = 1 - p(head)
p(tail) = 1 -0.3
p(tail) = 0.7
mark the brainliest plzz
Answer:
see below
Step-by-step explanation:
alaikum salam.
<u>2. </u><u>find</u><u> </u><u>cos Ф, sin Ф, tan Ф</u>
cos Ф = 5 / 13
Ф = 67.38
sin Ф = 12 / 13
Ф = 67.38
tan Ф = 12 / 5
Ф = 67.38
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<u>3. find sin β, cos β, tan β</u>
sin <u>β</u> = 4 / 5
<u>β</u> = 53.13
cos <u>β</u> = 3 / 5
<u>β</u> = 53.13
tan <u>β</u> = 4 / 3
<u>β</u> = 53.13
Answer:
the first triangle is 10
the second triangle is 8
Step-by-step explanation:
1. the formula for this is a²+b²=c²
c is the missing side
add in the numbers and you get 8²+6²=c²
8² is 64 and 6² is 36. 64+36 = 100
then find the square root of 100, which is 10
2. the formula for this is c²-b²=a²
17² - 15² = a²
289-225 = 64
the square root of 64 is 8
