The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.What is the probability that a randomly selected score is greater than 334? Write your answer as a decimal.

Using the normal distribution, it is found that there is a 0.0228 probability that a randomly selected score is greater than 334.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:[tex]Z = \frac{X - \mu}{\sigma}[/tex]The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, given by [tex]\mu = 310, \sigma = 12[/tex]The probability that a randomly selected score is greater than 334 is one subtracted by the p-value of Z when X = 334, hence:[tex]Z = \frac{X - \mu}{\sigma}[/tex][tex]Z = \frac{334 - 310}{12}[/tex]Z = 2Z = 2 has a p-value of 0.97721 - 0.9772 = 0.0228.0.0228 probability that a randomly selected score is greater than 334.More can be learned about the normal distribution at