51. 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?
Answer: B
The probability of the campaign receiving $50,000 should be determined using the Z-score.
To assess the likelihood of the campaign achieving at least $50,000 in donations, the Z-score is the appropriate measure. This statistical tool allows the organization to understand how many standard deviations the desired donation amount is from the mean donation amount.
A) Median
The median is a measure of central tendency that indicates the middle value of a dataset. While it provides insight into the typical donation amount, it does not help assess probabilities or the distribution of donations around the mean, making it unsuitable for determining the likelihood of reaching a specific total like $50,000.
B) Z-score
The Z-score is the correct choice because it quantifies how far a particular value (in this case, $50,000) is from the mean donation amount in terms of standard deviations. This helps the organization calculate the probability of achieving or exceeding the target amount based on the donations' mean and standard deviation.
C) R-squared
R-squared is a statistical measure that indicates the proportion of variance for a dependent variable that's explained by an independent variable or variables in a regression model. It is not relevant for this scenario, as the campaign does not involve regression analysis or the explanation of variance but rather the assessment of probabilities based on a normal distribution.
D) T-statistic
The T-statistic is used to determine whether there is a significant difference between the means of two groups, particularly when sample sizes are small. Since the question focuses on calculating probabilities based on a normal distribution rather than comparing means, the T-statistic is not applicable here.
Conclusion
The Z-score is the definitive measure for determining the probability of the campaign receiving at least $50,000, as it directly relates to the mean and standard deviation of the donation amounts. In contrast, the median, R-squared, and T-statistic do not provide the necessary insights for assessing the likelihood of achieving the targeted donation total. Thus, the Z-score is essential for making informed predictions in this context.