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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

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Answer:

55.563

Step-by-step explanation:

Given the following :

Mean(m) point = 73

Standard deviation( sd) = 10.6

Lower 5% will not get a passing grade (those below the 5% percentile)

For a normal distribution:

The z-score is given by:

z = (X - mean) / standard deviation

5% of the class = 5/100 = 0.05

From the z - table : 0.05 falls into - 1.645 which is equal to the z - score

Substituting this value into the z-score formula to obtain the score(x) which seperates the lower 5%(0.05) from the rest of the class

z = (x - m) / sd

-1.645 = (x - 73) / 10.6

-1 645 * 10.6 = x - 73

-17.437 = x - 73

-17.437 + 73 = x

55.563 = x

Therefore, the score which seperetes the lower 5% from the rest of the class is 55.563

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