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Answer:
0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.
This means that
Find the probability that an individual man’s step length is less than 1.9 feet.
This is the p-value of Z when X = 1.9. So
has a p-value of 0.0668
0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.
First, find the mean. You'll need it to compute the variance.
The variance of the sample is then computed with the formula
The standard deviation is the square root of the variance, so
The variance of the sample is then computed with the formula
The standard deviation is the square root of the variance, so