Question

Wering is an international study by unilever reveals that 40% of consumers are choosing to buy from brands they believe are doing social or environmental good. suppose you select a sample of 150 consumers. what is the probability that in the sample fewer than 38% are choosing to buy from brands they believe are or environmental good

Suppose you select a sample of 100 consumers
what is the probability that in the sample fewer than 30% are choosing to buy from brands they believe are doing social or environmental good?

Answer 1

To calculate the probability of a sample having fewer than a certain percentage of consumers choosing brands they believe to be doing good, use the normal approximation to the binomial distribution, applying the given population proportions to the specific sample sizes. Calculate the z-score and use a standard normal distribution to find the cumulative probability.

Step-by-step explanation:

The subject in question is concerning probability and statistics, specifically dealing with the population proportion and sampling distributions.

Finding the Probability

To find the probability of fewer than a certain percentage of a sample choosing to buy from brands they believe are doing social or environmental good, we would typically use the normal approximation to the binomial distribution since we are dealing with a large sample size (>30) and a population proportion (p) is given.

For the sample size of 150 consumers, if we want to find the probability that less than 38% choose socially or environmentally good brands, we first need to determine the expected number of consumers who would make such a choice based on the 40% statistic. This is done by multiplying 150 by 0.38, resulting in 57 consumers (expected value). However, since we're looking for fewer than 38%, we'd be interested in the cumulative probability of getting 56 or fewer consumers making this choice, which can be calculated using the normal approximation.

Similarly, for a sample size of 100 consumers, with fewer than 30% choosing such brands, we'd calculate the probability of getting 29 or fewer affirmative choices (since 30% of 100 is 30, and fewer than 30% means 29 or less), also using the normal approximation.

In both cases, after finding the z-score, we would use a standard normal distribution table or software to find the cumulative probability up to that z-score. Note: The use of the normal approximation assumes that the sample size is sufficiently large and both np and n(1-p) are greater than 5, which is a rule of thumb for when the normal approximation is appropriate.