A z-score is a means to compare rank from 2 different sets of data by converting the individual scores into a standard z-score. The formula to convert a value, X, to a z-score compute the following: find the difference of X and the mean of the date, then divide the result by the standard deviation of the data.
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z score = (test score - mean score)/SD z score = (87-81.1)/11.06z score = 5.9/11.06z score = .533You can use a z-score chart to calculate the probability from there.
A z-score of 0 means the value is the mean.
The z-score must be 1.87: the probability cannot have that value!
Z Score is (x-mu)/sigma. The Z-Score allows you to go to a standard normal distribution chart and to determine probabilities or numerical values.
You need to look up z-score tables.