At a Psychology final exam, the scores are normally distributed with a mean 73 points and a standard deviation of 10.6 points. The lower 5% of the class will not get a passing grade. Find the score that separates the lower 5% of the class from the rest of the class. 58.0 56.6 55.6 57.2

The score that separates the lower 5% of the class from the rest of the class is 55.6.

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 question:

Find the score that separates the lower 5% of the class from the rest of the class.

This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

The score that separates the lower 5% of the class from the rest of the class is 55.6.

1.8 or

the correct answer is 828.07