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Answer:
The score that cuts off the bottom 2.5% is 48.93.
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
What is the score that cuts off the bottom 2.5%
This is X when Z has a pvalue of 0.025, so X when Z = -1.96.
The score that cuts off the bottom 2.5% is 48.93.