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annabelle2516
01.07.2021 •
Mathematics
Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet. A sample of 45 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 1.9 feet. Round your answer to 4 decimal places, if necessary.
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Ответ:
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![\mu = 2.5, \sigma = 0.4](/tpl/images/1387/3597/915ca.png)
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
0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.
Ответ: