Answer to Question #268890 in Statistics and Probability for Harley

Question

6. A new rocket-launching system is being considered for deployment of small, short-range rockets. The existing system has p = 0.8 as the probability of a successful launch. A sample of 40 experimental launches is made with the new system, and 34 are successful. Using 95% confidence, the confidence interval is 0.85 + 0.111. What is the sample size required @ 90% level of confidence?

Answer 1

$$\hat{p}=\dfrac{34}{40}=0.85$$

$$z_c=1.6449$$

$$SE=z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

$$n=\dfrac{z_c^2\hat{p}(1-\hat{p})}{SE^2}$$

Given $SE=0.111$

$$n=\dfrac{(1.6449)^2(0.85)(1-0.85)}{(0.111)^2}=28$$