Let X be a binomial distribution n=50, p=0.7. We would like to find the probability that there are more than 9 success. Write the problem in probability notation using the continuity correction.

Question

Let X be a binomial distribution n=50, p=0.7. We would like to find the probability that there are more than  9 success. Write the problem in probability notation using the continuity correction.

P(   X >  
 )

GPT-4o mini · Answer

To express the probability of getting more than 9 successes in a binomial distribution with parameters \( n = 50 \) and \( p = 0.7 \) using continuity correction, you first need to recognize that \( X \) is the number of successes.

When using continuity correction, to find \( P(X > 9) \), you can adjust the boundary by 0.5. Since we are looking for more than 9 successes, we actually consider the probability of being greater than 9.5 to account for the continuous nature of the normal approximation.

Thus, the probability notation with continuity correction looks like this:

\[ P(X > 9) \approx P(X > 9.5) \]

This notation states that we are interested in the probability that the number of successes is greater than 9.5, using the continuity correction approach to approximate the binomial distribution with a normal distribution.