2.43. The level of college attainment (highest degree attained) of US population

Question

2.43. The level of college attainment (highest degree attained) of US population by racial and ethnic group in 1998 is given in the following tableb Percentage Racial or Eth nic Group Number of Adults Millions Percentage with Associate's Percentage with Bachelor's Degree with Graduate or Professional Degree Degree Native Americans Blacks Asians Hispanics Whites 1.1 16.8 4.3 11.2 132.0 6.4 5.3 7.7 4.8 6.3 6.1 7.5 22.7 5.9 13.9 3.3 3.8 13.9 3.3 7.7 The percentages given in the right three columns are conditional percentages a) How many Asians have had a graduate or professional degree in 1998? b) What percent of all adult Americans has had a Bachelor's degree as their highest? c) Given that the person's highest was an Associate's degree, what is the probability that the person was Hispanic?

Explanation / Answer

A=acceptence first college

B=acceptence second college

P(A)=0.6

P(B)=0.6

accepted in at least one college=acceptance in A and not acceptence in B+=acceptance in B and not acceptence in A+accepence in both A and B=P(A)*P(B')+P(A')*P(B)+P(A)*P(B)=0.6*0.4+0.6*0.4+0.6*0.6=0.84

or

we use binomial distribution with parameter n=2 and p=0.6 and for Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

X=acceptence in college

now P(non of the college give acceptence)=P(X=0)=0.16 ( using ms-excel command =BINOMDIST(0,2,0.6,0))

P(acceptence of at least one college)=1-P(X=0)=1-0.16=0.84

if there are 5 college we use binomial distribution with parameter n=5 and p=0.6

now P(non of the college give acceptence)=P(X=0)=0.01024 ( using ms-excel command =BINOMDIST(0,2,0.6,0))

P(acceptence of at least one college)=1-P(X=0)=1-0.01024 =0.98976

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