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Assume a random sample representative of the population is surveyed. If 36 people in the sample of size 117 are in favor, can the normal distribution approximation be used to estimate probabilities? (a) \( n p= \) (b) \( n(1-p)= \) (c) Yes, a normal distribution approximation can be used No, a normal distribution approximation can't be used

Ask by Weber Boone. in the United States
Mar 15,2025

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(a) \( n p = 36 \) (b) \( n(1 - p) = 81 \) (c) Yes, a normal distribution approximation can be used.

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To determine whether the normal distribution approximation can be used, we first need to calculate \( n p \) and \( n(1-p) \) using the sample data provided. (a) \( n p = 117 \times \frac{36}{117} = 36 \) (b) \( n(1-p) = 117 \times \frac{81}{117} = 81 \) With \( n p = 36 \) and \( n(1 - p) = 81 \), both values are greater than 5. Therefore, we can conclude that a normal distribution approximation can be used. (c) Yes, a normal distribution approximation can be used.

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