Answer
The range is from $1\;M\Omega-15\;M\Omega$.
Work Step by Step
This is an estimation problem. Consider each of the times to be the time constant, RC, for the timer circuit.
$$\tau=RC$$
Solve for the resistance.
$$R=\frac{\tau}{C}$$
Now estimate the needed resistances for each of the given times.
$$R_{1s}=\frac{\tau}{C}=\frac{1s}{1\times10^{-6}F}=1\times10^6\Omega$$
$$R_{2s}=\frac{\tau}{C}=\frac{2s}{1\times10^{-6}F}=2\times10^6\Omega$$
$$R_{4s}=\frac{\tau}{C}=\frac{4s}{1\times10^{-6}F}=4\times10^6\Omega$$
$$R_{8s}=\frac{\tau}{C}=\frac{8s}{1\times10^{-6}F}=8\times10^6\Omega$$
$$R_{15s}=\frac{\tau}{C}=\frac{15s}{1\times10^{-6}F}=15\times10^6\Omega$$
The range is from $1\;M\Omega-15\;M\Omega$.