The juror pool for the upcoming murder trial contains the names of 100000 indivi

Question

The juror pool for the upcoming murder trial contains the names of 100000 individuals. The proportion of Hispanics in this juror pool is 0.45. A jury of size 10 is selected at random from this list. Let X=the number of Hispanics selected to be jurors for this jury.

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Background: In Fall 2012 students in an introductory psychology class at MSU were surveyed about their non-academic internet use on portable electronic devices (cell phones, laptops, tablets). Non-academic activities were defined as internet shopping, reading the news, watching sports, and checking email. Students' responses about frequency of internet use (0, 1-3, 4-6, 7-9, almost all class) and duration (0, 1-5 min, 6-15 min, 16-30 min, > 30 min) were associated with their final exam scores. Internet use increased over the course of the semester. Higher rates of internet use were associated with lower test grades. This was independent of intellectual ability as measured by ACT scores.

In a study on internet usage and academic performance in second year undergraduate students, the performance (on a scale of 0-100) of high internet users was 12.1 points less than students without internet access (on a scale 0-100). There were 130 students who were high internet users. The proportion of high internet users performing worse than the comparison group was 56.3 %.

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Explanation / Answer

The standard deviation, SD=sqrt npq=sqrt (0.45*0.55*1000000)=157.32

The binomial model is expressed as (n,p) with n, the number of trials and p the probability of success. The distribution of X is binomial with n=100000, and p=0.45.

The mean, expected value of X is E(X)=np=100000*0.45=45000

P(X=3)=100000C3(0.45)^3(0.55)^99997=0.0000

P(X=0)=100000C0(0.45)^0(0.55)^100000=0.0000

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