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Ivan
2 years ago
12

In a recent​ year, an author wrote 169 checks. Use the Poisson distribution to find the probability​ that, on a randomly selecte

d​ day, he wrote at least one check.
Mathematics
1 answer:
grigory [225]2 years ago
8 0
We should first calculate the average number of checks he wrote per day.  To do that, divide 169 by 365 (the number of days in a year) and you get (rounded) 0.463.  This will be λ in our Poisson distribution.  Our formula is
P(X=k)= \frac{ \lambda ^{k}-e^{-\lambda} }{k!}.  We want to evaluate this formula for X≥1, so first we must evaluate our case at k=0.  
P(X=0)= \frac{0.463 ^{0}-e ^{-0.463} }{0!} \\ = \frac{1-e ^{-0.463} }{1} =0.3706
To find P(X≥1), we find 1-P(X<1).  Since the author cannot write a negative number of checks, this means we are finding 1-P(X=0).  Therefore we have 1-0.3706=0.6294.
There is a 63% chance that the author will write a check on any given day in the year.<em />
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\Rightarrow \theta=\dfrac{5}{6}\pi=\dfrac{5}{6}\times 180^{\circ}=150^{\circ}


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The vector ~v represents the displacement vector from Portland, Oregon to Houston, Texas. The vector w~ represents the displacem
Art [367]

Answer:

a

the displacement of the plane is  - \= w

b

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c

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Step-by-step explanation:

From the question we are the

   The displacement from Portland, Oregon to Houston, Texas. is  \= v

    The displacement  from Houston, Texas to Akron, Ohio.  is \= wa

a

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b

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c

From the question we are told that the plane flies over Portland to get to  Anchorage, Alaska which implies that it is moving in opposite direction to the vector \= v

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Then the vector which defines this displacement is mathematically represented as

   \= v + \= w  = 3000  -5500

    \= v + \= w  =- 2500 \ km

       

4 0
3 years ago
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