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Answer:
P(X > 126) = 0.2119
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
P(X > 126) is the 1 subtracted by the pvalue of Z when X = 126. So
[tez]Z = 0.8[/tex]
[tez]Z = 0.8[/tex] has a pvalue of 0.7881.
P(X > 126) = 1 - 0.7881 = 0.2119