Respuesta :
The given problem describes a binomial distribution with p = 60% = 0.6. Given that there are 400 trials, i.e. n = 400.
a.) The mean is given by:
[tex]\mu=np=400\times0.6=240[/tex]
The standard deviation is given by:
[tex]\sigma=\sqrt{npq} \\ \\ =\sqrt{np(1-p)} \\ \\ =\sqrt{400(0.6)(0.4)} \\ \\ =\sqrt{96}=9.80[/tex]
b.) The mean means that in an experiment of 400 adult smokers, we expect on the average to get about 240 smokers who started smoking before turning 18 years.
c.) It would be unusual to observe 340 smokers who started smoking before turning 18 years old in a random sample of 400 adult smokers because 340 is far greater than the mean of the distribution.
340 is greater than 3 standard deviations from the mean of the distribution.
a.) The mean is given by:
[tex]\mu=np=400\times0.6=240[/tex]
The standard deviation is given by:
[tex]\sigma=\sqrt{npq} \\ \\ =\sqrt{np(1-p)} \\ \\ =\sqrt{400(0.6)(0.4)} \\ \\ =\sqrt{96}=9.80[/tex]
b.) The mean means that in an experiment of 400 adult smokers, we expect on the average to get about 240 smokers who started smoking before turning 18 years.
c.) It would be unusual to observe 340 smokers who started smoking before turning 18 years old in a random sample of 400 adult smokers because 340 is far greater than the mean of the distribution.
340 is greater than 3 standard deviations from the mean of the distribution.
The Mean and standard deviation of random variable [tex]x[/tex] is [tex]240, 9.80[/tex] Respectively.
The given problem describes a binomial distribution with [tex]p=60 \% =0.6[/tex]
[tex]400[/tex] trials, i.e,[tex]n=400[/tex]
a)The mean is given by;
[tex]\mu =np[/tex]
[tex]\mu=400 \times 0.6[/tex]
[tex]\mu=240[/tex]
The standard deviation is given by the formula,
[tex]\sigma=\sqrt{npq}\\\sigma=\sqrt{np(1-p)\\[/tex]
[tex]\sigma=\sqrt{400(0.6)(0.4)}\\\sigma=\sqrt{96}[/tex]
[tex]\sigma=9.80[/tex]
b)The mean means that in an experiment of[tex]400[/tex] adult smokers,[tex]60\%[/tex] of adult smokers started smoking before turning [tex]18[/tex] years old so on an average [tex]240[/tex] smokers who started smoking before turning [tex]18[/tex] years.
c)It would be unusual to observe [tex]340[/tex] smokers who started smoking before turning [tex]18[/tex] years old in a random sample of [tex]400[/tex] adult smokers because [tex]340[/tex] is far greater than the mean of the distribution. [tex]340[/tex] is greater than the standard deviations from the mean of the distribution.
Learn more about Standard deviation concept here,
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