A nonprofit organization is asking for donations. It hopes to design an email campaign that will ensure it receives at least $50,000. The campaign will reach 10,000 donors and receive donations with a mean of $10 and a standard deviation of $5. Which measure should be used to determine the probability of the campaign receiving $50,000?

Rationale

Z-score

The Z-score is the appropriate measure to determine the probability of the campaign receiving $50,000, as it allows us to standardize the normal distribution of donations. By calculating the Z-score, we can find the likelihood of achieving a specific donation total based on the mean and standard deviation provided.

A (Z-score) CORRECT

The Z-score quantifies how many standard deviations an element is from the mean of a distribution. In this case, it can be calculated using the mean donation amount and standard deviation, allowing us to assess the probability of the campaign reaching the target of $50,000. Thus, it is the correct choice for evaluating the campaign's success.

B (T-statistic) YOUR ANSWER

The T-statistic is used primarily when dealing with small sample sizes or when the population standard deviation is unknown. In this scenario, the sample size is sufficiently large (10,000 donors), and the population standard deviation is given. Therefore, the T-statistic is not suitable for assessing the probability of reaching the donation goal in this context.

C (Median) YOUR ANSWER

The median represents the middle value of a data set when arranged in order. While it can provide some insight into the central tendency of donations, it does not convey information about the probability distribution needed to evaluate the likelihood of reaching a specific donation target like $50,000.

D (R-squared) YOUR ANSWER

R-squared is a statistical measure that represents the proportion of variance for a dependent variable that's explained by an independent variable(s) in a regression model. It is not applicable in this scenario, as we are not analyzing the relationship between variables but rather assessing the probability of achieving a specific total amount.

Conclusion

To evaluate the probability of the campaign receiving $50,000, the Z-score is the most suitable measure, allowing us to understand how the expected donations relate to the target. Other choices, such as the T-statistic, median, and R-squared, do not provide the necessary framework for this probability assessment. The Z-score's utility in standardizing the distribution makes it essential for determining the likelihood of reaching the fundraising goal.

Z-score

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