Wayne is solving a system of linear equations.
1 answer:
Answer:
(-2, 6.5)
Step-by-step explanation:
Wayne can follow the line from (-2, 0) up to where it crosses the graphed line. The crossing point is approximately halfway between 6 and 7 on the graph, so can be considered to be 6.5.
If we put x=-2 into the equation and evaluate, we get ...
... y = (-3/4)(-2) +5 = 6/4 +5 = (1 1/2) +5 = 6 1/2
Thus the solution is (-2, 6 1/2).
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Answer:
a) 9.52% probability that, in a year, there will be 4 hurricanes.
b) 4.284 years are expected to have 4 hurricanes.
c) The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
6.9 per year.
This means that
a. Find the probability that, in a year, there will be 4 hurricanes.
This is P(X = 4).
So
9.52% probability that, in a year, there will be 4 hurricanes.
b. In a 45-year period, how many years are expected to have 4 hurricanes?
For each year, the probability is 0.0952.
Multiplying by 45
45*0.0952 = 4.284.
4.284 years are expected to have 4 hurricanes.
c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here?
The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.