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According to a survey conducted in 2021 in Mexico, 70% of the inhabitants are cell phone users. If a sample of 100 people is taken… What is the probability that at least 30 are NOT cell phone users? Question 3Answer to. 30% b. 53.76% c. 70% d. 10.56% help me solve the problem

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Answer to a math question According to a survey conducted in 2021 in Mexico, 70% of the inhabitants are cell phone users. If a sample of 100 people is taken… What is the probability that at least 30 are NOT cell phone users? Question 3Answer to. 30% b. 53.76% c. 70% d. 10.56% help me solve the problem

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Santino
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To solve this problem, we can use the binomial probability formula to calculate the probability that at least 30 people in the sample are NOT cell phone users. The probability that a randomly chosen person is not a cell phone user is \(30\%\), or \(0.3\). We define:

- \(n = 100\), the sample size

- \(p = 0.3\), the probability of not being a cell phone user

The probability of having at least 30 people who are not cell phone users is computed as:

1. Calculate the cumulative probability of having fewer than 30 people who are not cell phone users using the binomial distribution:

P(X < 30) = \sum_{k=0}^{29} \binom{100}{k} (0.3)^k (0.7)^{100-k}

2. Subtract this cumulative probability from 1 to get the probability of having at least 30 people who are not cell phone users:

P(X \geq 30) = 1 - P(X < 30)

3. Use a calculator or statistical software to evaluate this sum:

P(X \geq 30) \approx 0.5376

Thus, the probability that at least 30 people in the sample are not cell phone users is approximately 53.76%

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