Answer:
95.86%.
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:
This probability is the pvalue of Z when subtracted by the pvalue of Z when
. So
X = 0.65
has a pvalue of 0.9793
X = 0.55
has a pvalue of 0.0207
So this probability is 0.9793 - 0.0207 = 0.9586 = 95.86%.