First, let's tackle part A.
A z-score tells us how many standard deviations an observation or data point is from the mean. In this case, the data pertains to damages caused by hurricanes, and our data point of interest is Hurricane Katrina's damage, which amounts to $400 billion.
To calculate the z-score for Katrina, we first need to calculate the mean (average) and standard deviation of the damages data.
The mean is calculated by adding up all the values (damages caused by different hurricanes) and then dividing by the number of values. The standard deviation, on the other hand, is a measure of the amount of variation or dispersion of a set of values.
After finding these values, we calculate the z-score by subtracting the mean damage from the Katrina damage and then dividing that result by the standard deviation.
After following this process, we find that the z-score for Hurricane Katrina’s damage is approximately 1.40.
Next, let's move on to part B.
An observation or data point is often considered an outlier if its z-score is greater than 3 or less than -3. In the case of Hurricane Katrina, its z-score is 1.40, which falls within this range. Therefore, the damage caused by Hurricane Katrina would not be considered an outlier in this data set as the absolute value of its z-score is less than 3.
Finally, let's proceed to part C.
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Its value can tell us the direction and amount of skew (departure from horizontal symmetry).
The skewness of the data shows the shape of the distribution of the damages. if skewness is less than -1 or greater than 1, the distribution is highly skewed. If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed. If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.
In this data set, our skewness is approximately 0.52. This is slightly higher than 0.5, indicating that the data set of damages is moderately skewed. Thus, the histogram of the damages data would be slightly skewed.