Respuesta :
Answer:
The probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.
Step-by-step explanation:
The random variable X can be defined as the number of adults questioned reported that their health was excellent.
A random sample of n = 11 adults are selected randomly selected from an area a nuclear power plant.
Of these 11 adults X = 3 reported that their health was excellent.
The proportion of adults who reported that their health was excellent is:
[tex]p=\frac{X}{n}=\frac{3}{11}[/tex]
An adult's health condition is not affected by others, i.e. they are independent.
The random variable X follows a Binomial distribution with parameters n = 11 and p = [tex]\frac{3}{11}[/tex].
The probability mass function of X is:
[tex]P(X=x)={11\choose x}(\frac{3}{11})^{x}(1-\frac{3}{11})^{11-x};\ x=0,1,2,3...[/tex]
Compute the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health as follows:
P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
[tex]=\sum\limits^{3}_{x=0}{{11\choose x}(\frac{3}{11})^{x}(1-\frac{3}{11})^{11-x}}\\=0.02998+0.12385+0.23254+0.26197\\=0.64834\\\approx 0.6483[/tex]
Thus, the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.
