True or False
For any normal distribution, the proportion in the tail beyond z = 2.00 is p = 0.0228.
true
Reiny
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True.
In a standard normal distribution, the proportion in the tail beyond z = 2.00 is approximately 0.0228. This means that approximately 2.28% of the data falls beyond z-score 2.00 in either the left or right tail.
To determine whether the statement is true or false, we need to refer to standard normal distribution tables or use statistical software.
The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1. It is commonly used to convert normal distributions into a standard form for analysis.
To find the proportion in the tail beyond a specific value, such as z = 2.00, we can use a standard normal distribution table or utilize statistical software. The table provides the area under the normal curve between the mean and the given z-score. However, to find the proportion beyond a specific z-score, we need to subtract the table value from 1.
Looking up z = 2.00 in a standard normal distribution table, we find that the proportion between the mean and z = 2.00 is approximately 0.9772. Thus, the proportion in the tail beyond z = 2.00 is 1 - 0.9772 = 0.0228.
Therefore, the statement is true.