I need help with this statistics and probability question

Question

In the country of the United States of height, Landia, the height measurements of 10 year old children are approximately normally distributed with a meaning of 55.9 inches in a standard deviation of 1.1 inches what is the probability that the height of a randomly chosen child between 53.25 and 55.15 inches do not round until you get your final answer and then round to three decimal places

Answer 1

mean = 55.9, standard deviation = 1.1

P(53.25<x<55.15)= ?

find the z scores for the endpoints

z = (x-mean)/s

z for 53.25 = (53.25-55.9)/1.1 = - 2.65/1.1 = about -2.4091

z for 55.15 = (55.15-55.9)/1.1 = -.75/1.1 = -75/110 = - 25/22 = about - .6818

find the corresponding areas under the curve from z crit to z=0 for each of the two above, then subtract their areas. use a z calculator or z tables

Areas =

.49361 - .25232

= .23929

= 23.929% of the randomly chosen 10 year old children, in Landia, will be between 55.15 and 53.25 inches

if your tables or calculator don't give more decimal places, as in the above calculations, then the final answer may be off by + or - .001% 23.929% is most likely, next best choices are 23.928 or 23.930%