Question

Find the indicated area under the curve of the standard normal​ distribution; then convert it to a percentage and fill in the blank. About​ ______% of the area is between zequalsminus3 and zequals3 ​(or within 3 standard deviations of the​ mean).

Answer 1

Answer:

About​ 99.74% of the area is between z = -3 and z = 3

Step-by-step explanation:

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.

Area between z = 3 and z = -3

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

0.9974*100 = 99.74%

About​ 99.74% of the area is between z = -3 and z = 3