Question

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

P(
<X<
)

Answer 1

To find the probability of getting exactly 9 successes in a binomial distribution with \( n = 50 \) and \( p = 0.7 \), we can use the continuity correction.

For a binomial distribution, the probability notation for exactly \( k \) successes is typically written as:

\[
P(X = k)
\]

However, when using the continuity correction for a normal approximation to the binomial distribution, we need to find the probability over an interval. Specifically, to approximate \( P(X = 9) \) using the normal distribution, we consider the interval \( (8.5, 9.5) \).

Thus, using probability notation with the continuity correction, we write:

\[
P(8.5 < X < 9.5)
\]

This interval accounts for the fact that we are looking for the exact value of 9 within a continuous approximation.

In conclusion, the probability notation with continuity correction is:

\[
P(8.5 < X < 9.5)
\]