8. Sampling Distributions & Confidence Intervals: Proportion
Sampling Distribution of Sample Proportion
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A previous study found that of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that, from this same random sample of people, that between and people prefer Coca Cola.
A
0.0125
B
0.9875
C
0.8
D
0.105
Verified step by step guidance1
Identify the problem as a binomial distribution problem where n = 100 and p = 0.2 (since 20% prefer Coca Cola).
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)).
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.
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.
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.
6:23mWatch next
Master Using the Normal Distribution to Approximate Binomial Probabilities with a bite sized video explanation from Patrick
Start learning
