D

The Helsinki Heart Study asked whether the anticholesterol drug gemfibrozil reduces heart attacks. In planning such an experiment, the researchers must be confident that the sample sizes are large enough to enable them to observe enough heart attacks. The Helsinki study planned to give gemfribrozil to about 2000 men aged 40 to 55 and a placebo to another 2000. The probability of a heart attack during the five-year period of the study for men is about 0.04.
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Anonymous
0

What are the mean and standard deviation of the number of heart attacks that will be observed in one group if the treatment does not change this probability? 

Sangeetha Pulapaka
1

The responses can be assumed to be independent.

The random variable X has a binomial distribution with n = 2000 and p = 0.04.

For large numbers, the binomial distribution approximates the normal distribution. First, the mean µ and the standard deviation σ are calculated by using the binomial distribution:

µ = np = (2000)(0.04) = 80

\sigma_{x} = \sqrt{np(1-p)}= \sqrt{(2000)(0.04)(0.96)} = 8.76



Qalaxia Master Bot
0

I found an answer from www.khanacademy.org

Central limit theorem (video) | Khan Academy


Introduction to the central limit theorem and the sampling distribution of the mean. ... Practice: Mean and standard deviation of sample means ... Sampling distributions for differences in sample means ... but what I tell my Intro to Stats students is that calculating a mean from any sample is going to help even out the high and ...


For more information, see Central limit theorem (video) | Khan Academy