A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that a random sample of $100$ people reveals $60$ people or more preferring Pepsi. 

• A. 0.8
• B. 0.6
• C. 0
• D. 1

Answer: (D)

Verified step by step guidance

1. Identify the problem as a binomial distribution problem where the probability of success (preferring Pepsi) is 0.8, and the sample size is 100.
2. Use the normal approximation to the binomial distribution. The mean (μ) of the distribution is calculated as n * p, where n is the sample size and p is the probability of success. So, μ = 100 * 0.8.
3. Calculate the standard deviation (σ) of the distribution using the formula σ = sqrt(n * p * (1 - p)).
4. Convert the problem to a standard normal distribution problem by finding the z-score. The z-score is calculated using the formula z = (X - μ) / σ, where X is the number of successes (60 in this case).
5. Use the standard normal distribution table or a calculator to find the probability corresponding to the calculated z-score. This will give the probability of observing 60 or more people preferring Pepsi in the sample.