(۷) =. What is g(۷) ?
1 answer:
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Answer:
The average number of days that will pass between measurable rain is 7.5.
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.
The expected period between the event happening is
During the dry month of August, one U.S. city has measurable rain on average only 4 days per month. Assume all months have 30 days.
This means that
(a) If the arrival of rainy days is Poisson distributed in this city during the month of August, what is the average number of days that will pass between measurable rain? *
The average number of days that will pass between measurable rain is 7.5.
Answer:
The answers to the question are
a) The probability that at most 1 person suffers side effect from the flu vaccine is 4.043×10⁻²
b) The probability that 4,5,or 6 persons suffer side effect from the flu vaccine is 0.49716.
Step-by-step explanation:
We solve the question using the formula for Poisson probability as follows
Let the probability of suffering a side effect from a certain flu vaccine be p
we have n = 1000 and p = 0.005
then by binomial theorem μ = 1000*0.005 = 5
using Poisson probability formula, we have
where λ = μ
for P(X=0) we have 6.73×10⁻³
P(X=1) we have 3.37×10⁻²
Using the addition rule, we have
P (X≤1) = P(X=0) + P(X=1) = 6.73×10⁻³ + 3.37×10⁻² = 4.043×10⁻²
b) Similarly, we have for k = 4, 5, 6 we have
P(X=4) we have 0.1755
P(X=5) we have 0.1755
P(X=6) we have 0.14622
Therefore P(X=4) or P(X=5), P(X=6) is given by
0.1755 + 0.17546 + 0.14622 = 0.49716