Consider a normal distribution that has n(55,7) (that is, a mean of 55 and a standard deviation of 7). to the nearest integer, the percentile rank of a value of 50 in this distribution is: a. 76 b. 48 c. 43 d. 24 e. 71

D. 24

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:

To the nearest integer, the percentile rank of a value of 50 in this distribution is:

This is the pvalue of Z when X = 50. So

has a pvalue of 0.2388.

So the correct answer is:

D. 24