8. Sampling Distributions & Confidence Intervals: Proportion
Sampling Distribution of Sample Proportion
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A previous study found that of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that a random sample of people reveals people or more preferring Pepsi.
A
0.8
B
0.6
C
0
D
1
Verified step by step guidance1
Identify the problem as a binomial distribution problem where n = 100 (sample size) and p = 0.8 (probability of preferring Pepsi).
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)).
Substitute the values into the formulas: μ = 100 * 0.8 and σ = sqrt(100 * 0.8 * 0.2).
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).
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.
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