Answer:
Measures equal or lower than 19.94 inches are significantly low.
Measures equal or higher than 25.06 inches are significantly high.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the back-to-knee lengths separating significant values from those that are not significant.
Significantly low
In this exercise, a value is going to be to significantly low if it has a pvalue of 0.01 or less. So we have to find X when Z has a pvalue of 0.01. This is between and , so we use
Measures equal or lower than 19.94 inches are significantly low.
Significantly high
In this exercise, a value is going to be to significantly high if it has a pvalue of 0.99 or more. So we have to find X when Z has a pvalue of 0.99. This is . So:
Measures equal or higher than 25.06 inches are significantly high.