Answer:
C. 59.01%
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 percentage of fourth graders are between 50 inches and 56 inches?
This is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.
X = 56
has a pvalue of 0.8729
X = 50
has a pvalue of 0.2843.
0.8729 - 0.2843 = 0.5886, which is close to 59.01%.
So the correct answer is:
C. 59.01%