A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment n=8, p=0.6, x<4

P ( X < 4 ) = 0.1736706  

Step-by-step explanation:

Given:

- A random variable X follows a binomial distribution as follows,  

                                Where n = 8, and p = 0.6.

Find:

- P ( X < 4 )?

Solution:

- The random variable X follows a binomial distribution as follows:

                                        X ~ B ( 8 , 0.6 )

- The probability mass function for a binomial distribution is given as:

                                pmf = n^C_r ( p )^r (1-p)^(n-r)

- We are asked to find P ( X < 4 ) which is the sum of following probabilities:

               P ( X < 4 ) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 )

- Use the pmf to compute the individual probabilities:

P ( X < 4 ) = 0.4^8 + 8^C_1*(0.6)*(0.4)^7 + 8^C_2*(0.6)^2*(0.4)^6 + 8^C_3*(0.6)^3*(0.4)^5 .

     P ( X < 4 ) = 6.5536*10^-4 + 7.86432*10^-3 + 0.04128768 +0.12386304

                     P ( X < 4 ) = 0.1736706  

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