Which of the following choices can be considered binomial random variables?
Choose all answers that apply:
A
A container holds 100 pens, half of which are red. Select an SRS of 5 pens and let R= the
number of red pens obtained.
в)
A container holds 1000 pens, half of which are red. Select an SRS of 5 pens and let S = the
number of red pens obtained.
A container holds 20 pens, half of which are red. Select an SRS of 5 pens and let Q = the
number of red pens obtained.

Q isn’t a binomial since the pens are being selected without replacement and the sample size is more than 10% of the population size, so the trails are not independent.

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MrRoyal MrRoyal · Answer 2 · 2021-12-13T03:40:30+01:00

A binomial random variable is such that can take either of two possibilities at the same time.

Samples R and S can be considered as binomial random variables

For a random variable to be considered a binomial random variable, the population must be at least ten times the sample size.

So, we have the following highlights

Container A

[tex]n =100[/tex]

[tex]x = 5[/tex]

Divide n by x

[tex]\frac nx = \frac{100}{5}[/tex]

[tex]\frac nx = 20[/tex]

This means that the population is 20 times the sample size.

Hence, R is a binomial random variable.

Container B

[tex]n =1000[/tex]

[tex]x = 5[/tex]

Divide n by x

[tex]\frac nx = \frac{1000}{5}[/tex]

[tex]\frac nx = 200[/tex]

This means that the population is 200 times the sample size.

Hence, S is a binomial random variable.

Container C

[tex]n =20[/tex]

[tex]x = 5[/tex]

Divide n by x

[tex]\frac nx = \frac{20}{5}[/tex]

[tex]\frac nx = 4[/tex]

This means that the population is 4 times the sample size.

Hence, Q is not a binomial random variable.

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