Respuesta :
Answer:
99.73
Step-by-step explanation:
Problems of normally distributed samples are 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.
Percentage within 3 standard deviations of the mean.
pvalue of Z = 3 subtracted by the pvalue of Z = -3.
Z = 3 has a pvalue of 0.9987
Z = -3 has a pvalue of 0.0013
0.9987 - 0.0013 = 0.9974 = 99.74%
A small rounding difference, but the answer is:
99.73
