Answer
a. $87$, $49$, $20$
b. 79
c. 75
d. 69
Work Step by Step
a. n=64,
for x=78 there are 55 numbers below so the percentile=$\frac{55+0.5}{64}\times100\approx87$
for x=66 there are 31 numbers below so the percentile=$\frac{31+0.5}{64}\times100\approx49$
for x=59 there are 12 numbers below so the percentile=$\frac{12+0.5}{64}\times100\approx20$
b. 90th percentile, position $c=\frac{64\times 90}{100}\approx 58$ gives a value of 79
c. 80th percentile, position $c=\frac{64\times 80}{100}\approx 51$ gives a value of 75
d. 65th percentile, position $c=\frac{64\times 65}{100}\approx 42$ gives a value of 69
