A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that, from this same random sample of $100$ people, that between $10$ and $11$ people prefer Coca Cola.

• A. 0.0125
• B. 0.9875
• C. 0.8
• D. 0.105

Answer: (A)

Verified step by step guidance

1. Identify the problem as a binomial distribution problem where n = 100 and p = 0.2 (since 20% prefer Coca Cola).
2. Use the normal approximation to the binomial distribution. Calculate the mean (μ) and standard deviation (σ) of the distribution: μ = np and σ = sqrt(np(1-p)).
3. Convert the binomial problem to a normal distribution problem by using the continuity correction. For the range 10 to 11, use 9.5 and 11.5.
4. Calculate the z-scores for 9.5 and 11.5 using the formula: z = (X - μ) / σ, where X is the value for which you are finding the z-score.
5. Use the standard normal distribution table to find the probabilities corresponding to the calculated z-scores and subtract to find the probability that between 10 and 11 people prefer Coca Cola.