Respuesta :
The mean is 36 and the standard deviation is 5.02.
The mean is given by
μ = np = 120*0.3 = 36.
The standard deviation is given by
σ = √(n*p*(1-p)) = √(120*0.3*0.7) = √25.2 = 5.02.
The mean is given by
μ = np = 120*0.3 = 36.
The standard deviation is given by
σ = √(n*p*(1-p)) = √(120*0.3*0.7) = √25.2 = 5.02.
Using the binomial distribution, it is found that:
- The mean of the number of smokers that will develop a sever lung condition is 36.
- The standard deviation is 5.02.
For each smoker, there are only two possible outcomes. Either they develop a severe lung condition, or they do not. The probability of a smoker developing a severe lung condition is independent of any other smoker, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The mean of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem:
- Probability of developing a disease is 0.3, hence [tex]p = 0.3[/tex].
- Sample of 120 smokers, hence [tex]n = 120[/tex].
Hence, the mean is:
[tex]E(X) = np = 120(0.3) = 36[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120(0.3)(0.7)} = 5.02[/tex]
A similar problem is given at https://brainly.com/question/24261244
