jaylanwest12
06.03.2020 •
Mathematics
A set of data values is normally distributed with a mean of 90 and a standard deviation of 4. Give the standard score and approximate percentile for a data value of 89.
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Ответ:
Standard score of -0.25.
A data value of 89 is approximately in the 40th percentile.
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:
Give the standard score and approximate percentile for a data value of 89.
Z when X = 89
has a pvalue of 0.4013.
So a data value of 89 is approximately in the 40th percentile.
Ответ: