Find the probability that 3 persons are 65 or older. Find

Chaya Galloway

Chaya Galloway

Answered question

2021-09-22

Find the probability that 3 persons are 65 or older.
Find the probability that 4 persons are 65 or older.

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2021-09-23Added 97 answers

Calculation:
Binomial probability:
Suppose X is a random variable with n trails and probability of success p, then probability of getting exactly k successes is,
P(X=k)=(nk)pk(1p)nk
The random variable X is defined as the number of senior citizens (aged 65 or older). A sample of 10 people is taken, that is n=10. The probability that people in the US are 65 years old or older is, p=0.13.
For 3 people to be 65 or older in US, substitute, n=10,p=0.13 and k=3 in binomial probability formula.
P(X=3)=(beg{array}{c}103end{array})(0.13)3(10.13)103
=120×0.02197×0.377254
=0.099
Hence, the probability that 3 persons are 65 or older is 0.099.
For 4 people to be 65 or older in US, substitute, n=10,p=0.13 and k=4 in binomial probability formula.
P(X=4)=(beg{array}{c}104end{array})(0.13)4(10.13)104
=210×0.00028561×0.4336262
=0.026
Hence, the probability that 4 persons are 65 or older is 0.026.

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