Assume a random sample representative of the population is surveyed. If 35 people in the sample of size 81 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

To determine whether you can use a normal distribution approximation, you need to check the conditions based on the sample size and the number of successes and failures. For \( n p \), where \( p \) is the sample proportion of successes: (a) \( n p = 81 \times \frac{35}{81} = 35 \) Now, for \( n(1-p) \): (b) \( n(1-p) = 81 \times \left(1 - \frac{35}{81}\right) = 46 \) Since both \( n p \) and \( n(1-p) \) are greater than 5, the normal distribution approximation can indeed be used to estimate probabilities. So, the answer is: (c) Yes, a normal distribution approximation can be used.