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disa [49]
3 years ago
15

A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the t

elevision leaves the factory. If the probability of passing these comprehensive tests is 0.95 and if 10 televisions are randomly selected what is that probability that at least 9 pass the test?
Mathematics
1 answer:
Vikki [24]3 years ago
7 0

Answer:

The value is   P(X \ge 9) = 0.9138

Step-by-step explanation:

From the question we are told that

  The probability of passing the test is  p =  0.95

  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)

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 \ge 9) =  P(X = 9 ) + P(X = 10 )

=> 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}]

=> P(X \ge 9) =  [0.3151] + [0.5987]

=> P(X \ge 9) = 0.9138

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