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 n = 100 (sample size) and p = 0.8 (probability of preferring Pepsi).
2. Use the normal approximation to the binomial distribution. Calculate the mean (μ) and standard deviation (σ) of the distribution using the formulas: μ = np and σ = sqrt(np(1-p)).
3. Substitute the values into the formulas: μ = 100 * 0.8 and σ = sqrt(100 * 0.8 * 0.2).
4. Convert the binomial problem to a normal distribution problem by finding the z-score for 60 people preferring Pepsi 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 60 or more people preferring Pepsi.