Respuesta :
Answer:
0.2835 = 28.35% probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals
Step-by-step explanation:
Mean during a time period means that we use the Poisson distribution.
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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
It is estimated that an average person makes four visits a year to doctors' offices and hospitals.
A year has 12 months, which means that the monthly mean is [tex]\mu = \frac{4}{12} = \frac{1}{3}[/tex]
What is the probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-(\frac{1}{3})}*(\frac{1}{3})^{0}}{(0)!} = 0.7165[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7165 = 0.2835[/tex]
0.2835 = 28.35% probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals
