Answer:
The value is ![P(X \ge 9) = 0.9138](https://tex.z-dn.net/?f=P%28X%20%5Cge%209%29%20%3D%200.9138%20)
Step-by-step explanation:
From the question we are told that
The probability of passing the test is ![p = 0.95](https://tex.z-dn.net/?f=p%20%3D%20%200.95)
The sample size is n = 10
Generally the distribution of the comprehensive testing of equipment follows a binomial distribution
i.e
![X \~ \ \ \ B(n , p)](https://tex.z-dn.net/?f=X%20%20%5C~%20%5C%20%5C%20%5C%20%20B%28n%20%2C%20p%29)
and the probability distribution function for binomial distribution is
![P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5E%7Bn%7DC_x%20%2A%20%20p%5Ex%20%2A%20%20%281-%20p%29%5E%7Bn-x%7D)
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that at least 9 pass the test is mathematically represented as
![P(X \ge 9) = P(X = 9 ) + P(X = 10 )](https://tex.z-dn.net/?f=P%28X%20%5Cge%209%29%20%3D%20%20P%28X%20%3D%209%20%29%20%2B%20P%28X%20%3D%2010%20%29)
=> ![P(X \ge 9) = [^{10}C_9 * (0.95)^9 * (1- 0.95)^{10-9}] + [^{10}C_{10} * (0.95)^{10} * (1- 0.95)^{10-10}]](https://tex.z-dn.net/?f=P%28X%20%5Cge%209%29%20%3D%20%20%5B%5E%7B10%7DC_9%20%2A%20%20%280.95%29%5E9%20%2A%20%20%281-%200.95%29%5E%7B10-9%7D%5D%20%2B%20%5B%5E%7B10%7DC_%7B10%7D%20%2A%20%20%280.95%29%5E%7B10%7D%20%2A%20%20%281-%200.95%29%5E%7B10-10%7D%5D)
=> ![P(X \ge 9) = [0.3151] + [0.5987]](https://tex.z-dn.net/?f=P%28X%20%5Cge%209%29%20%3D%20%20%5B0.3151%5D%20%2B%20%5B0.5987%5D%20)
=> ![P(X \ge 9) = 0.9138](https://tex.z-dn.net/?f=P%28X%20%5Cge%209%29%20%3D%200.9138%20)