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

Answer: P (X < 4) = 0.1736706