A study of community college enrollments in a certain state finds that 60% of al
ID: 3042316 • Letter: A
Question
A study of community college enrollments in a certain state finds that 60% of all full-time undergraduates are less than 20 years of age.
(a) If a random sample of four community college students is selected from this state, find the probability that at least three of the students are less than 20 years of age.
(b) Consider a random sample of 15 community college students from this state.
(i) What is the expected number of students under 20 years of age?
(ii) What is the standard deviation of the number of students under 20 years of age?
Explanation / Answer
X ~ binomial(n,p) = Binomial( 4 , 0.60)
Binomial probability distribution is
P(X) = nCx px (1-p)n-x
P(X >= 3) = P( X = 3) + P( X = 4)
= 4C3 0.603 0.40 + 4C4 0.604 0.400
= 0.4752
b)
n = 15,
X ~ Bin(15 , 0.60)
1)
Expected value = n p
= 15 * 0.60
= 9
ii)
Standard deviation = Sqrt( np ( 1-p) )
= Sqrt ( 15 * 0.6 * 0.4 )
= 1.8974
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