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Answer:
, which is greater than 0.01. So a back-to-knee length of 26.6 in. is not significantly high.
Step-by-step explanation:
Problems of normally distributed samples are 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:
In this problem, a value x is significantly high if:
Using these criteria, is a back-to-knee length of 26.6 in. significantly high?
We have to find the probability of the length being 26.6 in or more, which is 1 subtracted by the pvalue of Z when X = 26.6. So
has a pvalue of 0.9664.
1 - 0.9664 = 0.0336
, which is greater than 0.01. So a back-to-knee length of 26.6 in. is not significantly high.