The probability that a customer rates the logo as good is 0.42. Therefore, the probability that a customer does not rate the logo as good is 0.58.

The probability that none of the n customers rate the logo as good is given by:

\((0.58)^n\)

We want the probability that at least one person rates the logo as good to be greater than 0.995. Therefore, we have:

\(1 - (0.58)^n > 0.995\)

Rearranging gives:

\((0.58)^n < 0.005\)

Taking logarithms on both sides:

\(n \log(0.58) < \log(0.005)\)

Solving for n gives:

\(n > \frac{\log(0.005)}{\log(0.58)}\)

Calculating the right-hand side:

\(n > 9.727\)

Since n must be an integer, the smallest value of n is 10.