Quantitative Literacy Practice Exam

To how many standard deviations away from the mean is last year's rainfall of 49 inches?

1. 0.50

2. 0.24

3. 1.00

4. 0.45

The correct answer is: 0.24

To determine how many standard deviations last year's rainfall of 49 inches is away from the mean, you need to calculate the z-score. The z-score measures how many standard deviations a data point is from the mean and is calculated using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the value being measured (in this case, last year's rainfall of 49 inches), - \( \mu \) is the mean rainfall, - \( \sigma \) is the standard deviation of the rainfall. If, upon calculation, the z-score results in approximately 0.24, it means that the rainfall amount of 49 inches is 0.24 standard deviations below the mean. This reflects a relatively small deviation, indicating that last year's rainfall is close to the average yearly rainfall. The choice that corresponds to this calculation is thus accurate, depicting that last year's rainfall of 49 inches is indeed 0.24 standard deviations away from the mean. Understanding how to compute the z-score is crucial as it helps to understand the relative standing of a particular value within a distribution, showing whether it is above or below average and by how much in terms of the standard deviation