At a local community college, 57% of students who enter the college as freshmen

Question

At a local community college, 57% of students who enter the college as freshmen go on to graduate. Eight freshmen are randomly selected.

What is the probability that none of them graduates from the local college? (Round your intermediate calculations and final answer to 4 decimal places.)

What is the probability that at most seven will graduate from the local college? (Round your intermediate calculations and final answer to 4 decimal places.)

What is the probability that none of them graduates from the local college? (Round your intermediate calculations and final answer to 4 decimal places.)

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 0 ) = ( 8 0 ) * ( 0.57^0) * ( 1 - 0.57 )^8
= 0.0012
b)
P( X < = 7) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 8 7 ) * 0.57^7 * ( 1- 0.57 ) ^1 + ( 8 6 ) * 0.57^6 * ( 1- 0.57 ) ^2 + ( 8 5 ) * 0.57^5 * ( 1- 0.57 ) ^3 + ( 8 4 ) * 0.57^4 * ( 1- 0.57 ) ^4 + ( 8 3 ) * 0.57^3 * ( 1- 0.57 ) ^5 + ( 8 2 ) * 0.57^2 * ( 1- 0.57 ) ^6 + ( 8 1 ) * 0.57^1 * ( 1- 0.57 ) ^7 + ( 8 0 ) * 0.57^0 * ( 1- 0.57 ) ^8
= 0.9889

c)
Mean = 8 * 0.57 = 4.56

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.