Final answer:
The student's question requires calculating various probabilities for a sample proportion of a department store's credit sales, a statistical concept that involves knowledge of sampling distributions and normal approximation.
Step-by-step explanation:
The student's question involves determining the probability of certain outcomes for a sample proportion, given that a department store's credit sales are known to be 25% (0.25) of all sales. This is a statistical problem that can typically be solved using sampling distributions, namely the binomial or normal distribution approximation depending on the sample size and the probability in question.
To answer the student's specifics:
- For (a), one would calculate the probability that the sample proportion of credit sales in a sample of 75 sales is greater than 0.33.
- For (b), the probability that the sample proportion falls between 0.191 and 0.355 needs to be found.
- For (c), the probability of the sample proportion being greater than the known population proportion of 0.25 is sought.
- For (d), the task is to determine the probability that the sample proportion is less than 0.14.
Each of these requires calculation using normal approximation to the binomial distribution if the sample size is sufficiently large and the sample proportion is not too close to 0 or 1.