Question

A survey found that 27% of consumers from a country A are more likely to buy stock in a company based in country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a sample of 200 respondents from country A.

a) What is the probability that in the sample, between 24% and 28% are more likely to buy stock in a company based in country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
b) What is the probability that in the sample, more than 30% are more likely to buy stock in a company based in country A, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
c) How will your answer in part b change if you have a sample of 600?

Answer 1

To calculate the probability, we can use the binomial distribution formula. a) Find the probability of between 24% and 28%. b) Find the probability of more than 30%. c) Calculate the probability with a sample size of 600.

Step-by-step explanation:

To calculate the probability, we can use the binomial distribution formula. In this case, the probability of success (p) is 0.27, and the sample size (n) is 200.

a) To find the probability that between 24% and 28% are more likely to buy stock or shop at its stores, we need to find the cumulative probability of both percentages. Calculate the probability of each percentage using the binomial formula, and subtract the lower cumulative probability from the higher one.

b) To find the probability that more than 30% are more likely to buy stock or shop at its stores, we need to find the cumulative probability of 30% and subtract it from 1 to get the complementary probability.

c) If the sample size increases to 600, the probability can be calculated using the same formula with a different sample size.