What proportion of observations from the standard normal distribution are greater that 2.88?
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To find the proportion of observations from the standard normal distribution that are greater than 2.88, we need to use a standard normal table or a statistical software program, as the calculations can be quite complex.
Using a standard normal table, we can find the area under the curve to the left of 2.88. Subtracting this area from 1 will give us the proportion of observations greater than 2.88.
Looking up the z-score for 2.88 in the standard normal table, we find that the z-score is approximately 0.9977.
Thus, the proportion of observations from the standard normal distribution that are greater than 2.88 is approximately 1 - 0.9977 = 0.0023, or 0.23%.
To find the proportion of observations from the standard normal distribution that are greater than 2.88, we need to use a standard normal table or a statistical calculator.
A standard normal table provides the cumulative probability for a given value (z-score) in the standard normal distribution. The z-score represents the number of standard deviations an observation is from the mean.
First, we find the z-score corresponding to the value 2.88. The z-score formula is:
z = (x - μ) / σ
Given that we are dealing with the standard normal distribution, the mean (μ) is 0 and the standard deviation (σ) is 1. Plugging in the values:
z = (2.88 - 0) / 1 = 2.88
Next, we need to find the proportion of observations with a z-score greater than 2.88. In the standard normal table, we look for the value closest to 2.88. The table provides the cumulative probabilities for z-scores up to a certain value.
For example, if the closest value in the table is 2.89, we see that the cumulative probability associated with a z-score of 2.89 is 0.9986. This means that approximately 99.86% of the observations in the standard normal distribution have a z-score less than or equal to 2.89.
Since we want to find the proportion of observations with a z-score GREATER than 2.88, we need to subtract the cumulative probability from 1:
Proportion = 1 - 0.9986 = 0.0014
Therefore, approximately 0.14% of observations from the standard normal distribution are greater than 2.88.