Let x be normally distributed with mean µ = 25 and standard deviation σ = 5. find the value x such that p(x ≥ x) = 0.1736

The score is X = 29.7.

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 problem, we have that:

Find the value x such that p(x ≥ x) = 0.1736.

This is X when Z has a pvalue of 1-0.1736 = 0.8264. So it is X when Z = 0.94. So

The score is X = 29.7.