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Census data shows that 30% of residents of Squirfornal County are black. A pool of potential jurors is to be selected for a trial. Names of Squirfornal County residents are drawn one by one to make up the pool of potential jurors. the first twelve whose names were drawn are seated and interviewed to see if they would be appropriate for the jury.find the probability that this group of 12 potential jurors contains... HINT: the selection of each juror can be considered a Bernoulli trial which is a 'success' if the potential juror is black a)... exactaly three black potential jurors b) ...four or fewer black potential jurors c) ...fewer than two black potential jurors

Question

Census data shows that 30% of residents of Squirfornal County are black. A pool of potential jurors is to be selected for a trial. Names of Squirfornal County residents are drawn one by one to make up the pool of potential jurors. the first twelve whose names were drawn are seated and interviewed to see if they would be appropriate for the jury.

find the probability that this group of 12 potential jurors contains... HINT: the selection of each juror can be considered a Bernoulli trial which is a 'success' if the potential juror is black

 

a)... exactaly three black potential jurors

 

b) ...four or fewer black potential jurors

 

c) ...fewer than two black potential jurors

 

check_circleAnswer
Step 1

It is given that 30% of residents of the country are black. Therefore, probability of a randomly selected resident being black is 0.30. Also it is given that the selection of each juror can be considered as a Bernoulli trial. Therefore, the random variable X, number of black potential jurors follows a binomial distribution with n=12 and p=0.30.

Step 2

a.

The probability that the group of 12 potential jurors contains exactly 3 black potential jurors can be calculated by entering the formula ‘=BINOM.DIST(3,12,0.3,FALSE)’ in EXCEL software.

fix
-BINOM.DIST(3,12,0.3, FALSE)
A1
A
C
0.239700426
1
help_outline

Image Transcriptionclose

fix -BINOM.DIST(3,12,0.3, FALSE) A1 A C 0.239700426 1

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Step 3

b.

The probability that the group of 12 potential jurors contains 4 or fewer black potential jurors can be calculated by ...

fox
BINOM.DIST(4,12,0.3,TRU E)
A1
A
C
D
F
0.72365547
1
help_outline

Image Transcriptionclose

fox BINOM.DIST(4,12,0.3,TRU E) A1 A C D F 0.72365547 1

fullscreen

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