Answer :
Final answer:
The combined probability that Z is less than 1.57 or greater than 1.84 in a standardized normal distribution is 0.975 or 97.5%.
Explanation:
The question pertains to a concept in statistics known as the Standardized Normal Distribution or Z-Score. To find the probability that Z is either less than 1.57 or greater than 1.84, we need to look up these values in a Z-table, which provides the area to the left of a given Z-score in a standard normal distribution. However, since the Z-tables typically only give us “less than”, to determine the 'greater than' we need to subtract the 'less than' from 1. For example, if the value listed for 1.57 is 0.942, then the probability of Z being less than 1.57 equals 0.942.
Similarly, for Z being greater than 1.84, if the Z-table lists the value for 1.84 as 0.967, the probability of Z being greater than 1.84 is 1 - 0.967 = 0.033. Therefore, the combined probability that Z is less than 1.57 or greater than 1.84 is 0.942 + 0.033 = 0.975 or 97.5%.
Learn more about Standardized Normal Distribution here:
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