From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271 .
6 out of 10 Niceville residents shop at Walmart
So, the probability of shopping at Walmart (p) is = 6/10 = 0.6
The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .
The number of members in the group is(n) = 15 ;
We have to find the probability that, at least thirteen of them shop at Walmart
By the Binomial Probability Distribution,
we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ
So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)
Substituting the values of a , n and p and q ,
We get ;
= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰
= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰
= 0.0219 + 0.0047 + 0.0004
= 0.0271
Therefore, the required probability is 0.0271
Learn more about Binomial Probability Distribution here
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