Answer:
The value is [tex]P(X \ge 9) = 0.9138 [/tex]
Step-by-step explanation:
From the question we are told that
The probability of passing the test is [tex]p = 0.95[/tex]
The sample size is n = 10
Generally the distribution of the comprehensive testing of equipment follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
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
[tex]P(X \ge 9) = P(X = 9 ) + P(X = 10 )[/tex]
=> [tex]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}][/tex]
=> [tex]P(X \ge 9) = [0.3151] + [0.5987] [/tex]
=> [tex]P(X \ge 9) = 0.9138 [/tex]
