Math home work standard deviation word problem

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 10.8 inches, and standard deviation of 1.9 inches.

If one item is chosen at random, what is the probability that it is less than 13.6 inches long? Express your answer in decimal form.

Answer 1

(13.6 - 10.8)/1.9 = 2.8/1.9 = 2 standard deviations from the mean = z

use the empirical rule, 68-95-99.7 for 1, 2 and 3 standard deviations from the mean

95% of the lengths fall within 2 standard deviations from the mean.

the 5% not within 2 SD is half above 2 SD and half below

.025 is above 13.8. 97.5% is less than 13.8

97.5% = 0.975