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Answer:
The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
X ~ N(77,8).
This means that
Z-score when X = 76:
Negative means that its to the left of the mean.
The Z-score when x = 76 is of -0.125, which tells you that x = 76 is 0.125 standard deviations to the left of the mean.