You are performing a cohort study to look at risk factors for breast cancer in postmenopausal women. 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.
5±60
10±6
5±2
10±5
5±6
To calculate the expected value and standard deviation in this case, we need to use the probability of developing breast cancer among smokers and the sample size.
The expected value (mean) can be found by multiplying the probability by the sample size:
Expected Value = Probability of developing breast cancer among smokers * Sample size
Expected Value = 0.05 * 100 = 5
So, we expect 5 smokers to develop breast cancer.
To find the standard deviation, we can use the formula:
Standard Deviation = √(Probability * (1 - Probability) * Sample size)
Standard Deviation = √(0.05 * (1 - 0.05) * 100) = √(0.05 * 0.95 * 100) = √4.75 ≈ 2.18
Approximating the standard deviation to 1 decimal place, we can say it is approximately 2.2.
Therefore, the answer is: 5±2.2.