Question

A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the television leaves the factory. If the probability of passing these comprehensive tests is .95 and if 10 televisions are randomly selected what is that probability that at least 9 pass the test

Answer 1

Answer:

The probability is   $P(X \le 9) =0.9138$

Step-by-step explanation:

From the question we are told that

   The probability of the television passing the test is  p = 0.95

    The sample size is  n  =  10

Generally the comprehensive testing process for all essential functions  follows a binomial distribution  

i.e  

         $X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial  distribution is  

      $P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

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

     $P(X \le 9) = P(X = 9) + P(X = 10 )$

=>  $P(X \le 9) = [^{10}C_9 * (0.95)^9 * (1- 0.95)^{10-9}]+ [^{10}C_{10} * {0.95}^{10} * (1- 0.95)^{10-10}]$

=> $P(X \le 9) = [10 * 0.6302 * 0.05 ]+ [1 *0.5987 * 1 ]$

=> $P(X \le 9) =0.9138$