A community college has a math placement exam that has a mean of 65 and a standard deviation of 8.2. If a student takes the exam and scores in the lower 2.5%, they are eligible for a free intensive course to help them succeed in their math class. Assume that the exam has a normal distribution. What is the score that cuts off the bottom 2.5%

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.