Answer:
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 25, \sigma = 5[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.94 = \frac{X - 25}{5}[/tex]
[tex]X - 25 = 5*0.94[/tex]
[tex]X = 29.7[/tex]
The score is X = 29.7.
