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Answer :
Approximately 94.18% of observations have a z-score less than 1.57 in a normally distributed data set.
To find the proportion of observations with a z-score less than 1.57 in a standard normal distribution, we can use a standard normal distribution table or a statistical calculator.
The proportion of observations corresponds to the cumulative probability of the z-score. In this case, we want to find the cumulative probability up to a z-score of 1.57.
Using the standard normal distribution table or a calculator, we find that the cumulative probability associated with a z-score of 1.57 is approximately 0.9418.
Rounding to four decimal places, the proportion of observations with a z-score less than 1.57 is 0.9418.
Therefore, approximately 0.9418 (or 94.18%) of observations have a z-score less than 1.57 in a normally distributed data set.
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