Answer:
[tex]P(x=3) = 0.1318[/tex]
Step-by-step explanation:
The question illustrates a binomial distribution and the given parameters are:
Given
[tex]n = 6[/tex] -- sample size
[tex]p = 0.75[/tex] --- probability of success
[tex]r = 3[/tex] --- half of the participant
Using the binomial probability formula, we have:
[tex]P_x = ^nC_xp^x(1-p)^{n-x}[/tex]
For x = 3, the probability is:
[tex]P(x=3) = ^6C_3*0.75^3 * (1-0.75)^{6-3}[/tex]
[tex]P(x=3) = 20*0.75^3 * 0.25^3[/tex]
[tex]P(x=3) = 0.1318[/tex]
