Answer: 0.0014
Step-by-step explanation:
In binomial probability distribution , The probability of getting success in x trials (where x is a binomial variable ) :
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
, where p= probability of getting success in each trial.
n= Total number of trials.
Given : The proportion of students who enter the college as freshmen go on to graduate : p= 0.56
Sample size : n= 8
Let x represents the students in the college who enter the college as freshmen go on to graduate.
Then, the probability that none of them graduates from the local community college will be :_
[tex]P(x=0)=^{8}C_0(0.56)^{0}(1-0.56)^8\\\\=(1)(0.44)^8\ \ [\because\ ^nC_0=1 ]\\\\=0.00140482236252\approx0.0014[/tex]
Hence, the required probability =0.0014
