Consider a normal distribution with mean 23 and standard deviation 7. What is the probability a value selected at random from this distribution is greater than 23? (Round your answer to two decimal places.)

0.5 = 50% probability a value selected at random from this distribution is greater than 23

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:

What is the probability a value selected at random from this distribution is greater than 23?

This is 1 subtracted by the pvalue of Z when X = 23. So

has a pvalue of 0.5

0.5 = 50% probability a value selected at random from this distribution is greater than 23