Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

The minimum score needed to be accepted is 525.3.

Step-by-step explanation:

Problems of normally distributed samples are 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 problem, we have that:

If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

The 60th percentile, which is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.253. So

The minimum score needed to be accepted is 525.3.

step-by-step explanation:

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