Which steps should be used to compare the fractions StartFraction 2 Over 9 EndFraction and StartFraction 5 Over 6 EndFraction? F
2 answers:
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Answer:
a) 19.85% probability that a total of two people are struck by lightning during first four months of the year.
b) 22.68% probability that the year has 5 good and 7 bad months
Step-by-step explanation:
We are going to use the Poisson distribution and the binomial distribition to solve this question.
Poisson distribution:
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.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
a.Find the probability that a total of two people are struck by lightning during first four months of the year.
10 people during a year(12 months).
In 4 months, the mean is
This is P(X = 2).
19.85% probability that a total of two people are struck by lightning during first four months of the year.
b.Say that a month is good is no one is struck by lightning, and bad otherwise. Find the probability that the year has 5 good and 7 bad months.
Probability that a month is good.
P(X = 0), Poisson
The mean is
Find the probability that the year has 5 good and 7 bad months.
Now we use the binomial distribution, we want P(X = 5) when n = 12, p = 0.4346. So
22.68% probability that the year has 5 good and 7 bad months