Question

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

P( X>

Answer 1

To find the probability of obtaining at least 9 successes in a binomial distribution with parameters \( n = 50 \) and \( p = 0.7 \), we can express this in probability notation as follows:

We are interested in \( P(X \geq 9) \).

Using the continuity correction, since the binomial distribution is discrete, we convert this to a normal approximation:

\[ P(X \geq 9) = P\left(X > 8.5\right) \]

Thus, the problem in probability notation using the continuity correction is:

\[ P(X > 8.5) \]

This approximates the probability using the normal distribution, which is valid when \( n \) is large and \( p \) is not too close to 0 or 1. To compute this, you would typically standardize and use the Z-table or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.