Answer :
Final answer:
The probability of getting 116 or fewer smartphone owners who use them in theaters is approximately 0.5031.
Explanation:
To find the probability of getting 116 or fewer smartphone owners who use them in theaters, we can use the binomial probability formula. The formula is: P(X ≤ k) = Σ[(nCk)(p^k)(q^(n-k))], where n is the sample size (279), k is the number of successes (116), p is the probability of success (0.42), and q is the probability of failure (1 - p). We can calculate the probability using this formula:
- P(X ≤ 116) = Σ[(279C0)(0.42^0)(0.58^(279-0))] + Σ[(279C1)(0.42^1)(0.58^(279-1))] + ... + Σ[(279C116)(0.42^116)(0.58^(279-116))]
- P(X ≤ 116) = 0.5031
Therefore, the probability of getting 116 or fewer smartphone owners who use them in theaters is approximately 0.5031.
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