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 conditions are met to use a normal distribution approximation for the proportion of skin biopsies that came back as melanoma, we need to check the following conditions: 1. \( n p \) should be greater than or equal to 10. 2. \( n (1 - p) \) should also be greater than or equal to 10. Where: - \( n \) is the number of biopsies (116 in this case). - \( p \) is the proportion of biopsies that came back as melanoma (0.014). Let's calculate \( n p \) and \( n (1 - p) \): 1. Calculate \( n p \): \[ n p = 116 \times 0.014 \] 2. Calculate \( n (1 - p) \): \[ n (1 - p) = 116 \times (1 - 0.014) \] Now, I will perform these calculations. Calculate the value by following steps: - step0: Calculate: \(116\times 0.014\) - step1: Multiply the numbers: \(1.624\) Calculate or simplify the expression \( 116 * (1 - 0.014) \). Calculate the value by following steps: - step0: Calculate: \(116\left(1-0.014\right)\) - step1: Subtract the numbers: \(116\times 0.986\) - step2: Multiply the numbers: \(114.376\) Now that we have performed the calculations, we can summarize the results: 1. \( n p = 116 \times 0.014 = 1.624 \) 2. \( n (1 - p) = 116 \times (1 - 0.014) = 114.376 \) Next, we check the conditions: - \( n p = 1.624 \) (which is less than 10) - \( n (1 - p) = 114.376 \) (which is greater than 10) Since \( n p < 10 \), the conditions are **not met** to use a normal distribution approximation. Thus, the conclusion is: - The conditions are **not met**.