p-value in a binomial test

Question 1

In a hypothesis test, a manufacturer claims that a proportion p of its bulbs last more than 1000 hours. A random sample of 23 bulbs is taken and 11 of them last more than 1000 hours. The hypotheses are $H_{0}: p = 0.7$ and $H_{1}: p < 0.7$, and the test is at the 5% significance level. Let $X$ be the number of the 23 bulbs that last more than 1000 hours. Assuming $H_{0}$ is true, find $P(X \le 11)$. Give your answer to 4 decimal places.