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

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%