Using the normal distribution, it is found that the proportion is closest to 0.023, given by option d.
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Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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- Mean of 25 means that [tex]\mu = 25[/tex]
- Standard deviation of 4 means that [tex]\sigma = 4[/tex].
- The proportion above 33 is 1 subtracted by the p-value of Z when X = 33, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 25}{4}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.977.
1 - 0.977 = 0.023
Thus the proportion is 0.023, given by option d.
A similar problem is given at https://brainly.com/question/15181104
