When a dermatologist suspects that skin may show signs of disease or cancer they will likely take a skin biopsy for analysis. This process involves removing a small portion of the affected skin. In a 2017 study, the proportion of skin biopsies that came back as melanoma was \( p=0.014 \). If the study included 116 biopsies, are the conditions met to use a normal distribution approximation? \( n p= \) and \( n(1-p)= \) The conditions are met Submit

To determine if the normal approximation can be used for the binomial distribution in this scenario, we calculate \( n p \) and \( n(1-p) \). With \( n = 116 \) and \( p = 0.014 \): - \( n p = 116 \times 0.014 = 1.624 \) - \( n(1-p) = 116 \times (1 - 0.014) = 116 \times 0.986 = 114.776 \) Since \( n p < 5 \) and \( n(1-p) > 5 \), the conditions for using the normal approximation are not fully satisfied. Therefore, we would need to use the binomial distribution for more accurate results. Although the normal approximation may not apply perfectly in this case, you can still analyze binomial data through alternative methods such as simulations or exact calculations. Just keep in mind that for smaller probabilities and samples, relying on the actual distribution is usually the best course of action!