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If the probability of developing breast cancer among smokers is .05 for the study duration, then if you sample 100 smokers, how many do you expect to develop the disease? Give the expected value +/- 1 standard deviation.

Respuesta :

JeanaShupp

Answer: [tex]5\pm2[/tex]

Explanation:

Given : The probability of developing breast cancer among smokers : [tex]p=0.05[/tex]

Sample size = 100

The mean  for binomial distribution is given by :-

[tex]\mu=np=0.05\times100=5[/tex]

The standard deviation for binomial distribution is given by :-

[tex]\sigma=\sqrt{np(1-p)}[/tex]

[tex]\Rightarrow\sigma=\sqrt{100(0.05)(1-0.05)}\\\\\Rightarrow\sigma=2.1794494717\approx2[/tex]

The expected number of people will develop the disease is given by :-

[tex]\mu\pm\sigma=5\pm2[/tex]

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