A placement test for state university freshmen has a normal distribution with a mean of 600 and a standard deviation of 30. The bottom 4% of students must take a summer session. What is the minimum score you would need to stay out of this group?
Answer (2)
To stay out of the bottom 4% of students on the placement test, a student needs to score at least 548. This calculation is based on the normal distribution mean of 600 and a standard deviation of 30. The Z-score for the 4th percentile, approximately -1.75, helps us find the minimum required score.
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To determine the minimum score required to stay out of the bottom 4% of students in a normally distributed placement test, we need to find the score that corresponds to the 4th percentile.
The test scores follow a normal distribution with a mean ( μ ) of 600 and a standard deviation ( σ ) of 30.
We need to find the Z-score that corresponds to the bottom 4% of a standard normal distribution. Typically, the Z-score for the 4th percentile is approximately -1.75. This value can be found using a Z-table or statistical software.
The formula to convert a Z-score to an actual score (X) in a normal distribution is:
X = μ + Z × σ
Substituting the known values:
X = 600 + ( − 1.75 ) × 30
Calculate the score:
X = 600 − 52.5 = 547.5
Therefore, the minimum score needed to stay out of the bottom 4% of students is approximately 548.
