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
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Mind Expander
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.