Answer
a. $166000\ \Omega $.
b. $996000\ \Omega.$
c. $664000\ \Omega.$
d. $ 332000\ \Omega$.
Work Step by Step
a. The black fourth band indicates a tolerance of $\pm 20\%$.
$$20\% \times 830,000\Omega = (0.20)(830,000\Omega) =166000\ \Omega .$$
That is, the tolerance is $166000\ \Omega $.
b. The upper limit is
$$830,000\ \Omega + 166,000 \ \Omega=996000\ \Omega.$$
c. The lower limit is
$$830,000\ \Omega + 166,000 \ \Omega=664000\ \Omega.$$
d. The tolerance interval is then $$
996000 \ \Omega-664000\ \Omega= 332000\ \Omega
.$$
