Final answer:
The question deals with the computation of specific percentiles for human pregnancy lengths using the properties of the normal distribution, mean, and standard deviation to identify the range for the middle 90%, the shortest 2.5%, and the longest 4% of pregnancies.
Step-by-step explanation:
The question concerns the normal distribution of human pregnancy lengths, which have a mean of 266 days and a standard deviation of 16 days. To determine the range for the middle 90% of all pregnancies, we need to find the z-scores that correspond to the 5th and 95th percentiles because these will delineate the lower and upper bounds of the middle 90%. The z-scores for these percentiles can be found using a standard normal distribution table or a calculator equipped with statistical functions.
To find out how long the shortest 2.5% of all pregnancies last, we will look for the z-score that corresponds to the 2.5th percentile. Similarly, to know how long the longest 4% of pregnancies last, we'll identify the z-score for the 96th percentile. These z-scores can then be used to calculate the specific number of days by transforming them back into the corresponding values using the normal distribution's mean and standard deviation.