Respuesta :
Answer:
D. 24
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 = 55, \sigma = 7[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 55}{7}[/tex]
[tex]Z = -0.71[/tex]
[tex]Z = -0.71[/tex] has a pvalue of 0.2388.
So the correct answer is:
D. 24
