Answer:
[tex]X = 30[/tex]
Step-by-step explanation:
Problems of normally distributed samples are 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]Z = -0.5, \mu = 35, \sigma = 10[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.5 = \frac{X - 35}{10}[/tex]
[tex]X - 35 = -0.5*10[/tex]
[tex]X = 30[/tex]
