(a) We need to figure out the deciles for a normal distribution curve in this part.
In order to do so, we need to find the z score corresponding to probability 0.10 and 0.90 on the normal distribution curve.
Upon looking at the normal distribution table, we can see that the probability P = 0.10 corresponds to a z score of -1.28 and probability P = 0.90 corresponds to a z score of 1.28.
Therefore, deciles are -1.28 and 1.28 for a normal distribution curve.
(b) In this part, we are given that mean height is 69.5 inches and standard deviation in height is 2.7 inches. Therefore, we can find the deciles using the z score formula as shown below:
Therefore, the required deciles are 66.044 and 72.956