Answer: for 10th percentile, X = 60.53inches
for 80th percentile, X = 61.53 inches
Explanation:
the relationship between the mean, standard deviation and the standard normal distribution is given as
X = μ + σZ
where μ is the mean and σ is the standard deviation of the variable X, and Z is the value from the standard normal distribution for the desired percentile.
Hence to determine the 10th and 80th percentile, we lookup the standard normal distribution table attached below,
from the table,
at 10th percentile Z = -1.282
at 80th percentile we interpolate between 75th percentile and 90th
(80 - 75)/(90 - 75) = (Z - 0.675)/(1.282 - 0.675)
5/15 = Z - 0.675/0.607
0.333*(0.607) = Z - 0.675
Z = 0.8771
hence the Z value for the 80th percentile is 0.8771
hence
X value for 10th percentile and 80th is calculated as
X = μ + σZ
since mean = 63.7 and standard deviation = 2.47
For 10th percentile
X = 63.7 + 2.47*(-1.282)
X = 60.53
for 80th percentile
X = 63.7 + 2.47*(0.8771)
X = 61.53