Step 1 :Calculate the standard error of the mean using the formula \(SE = \frac{\sigma}{\sqrt{n}}\). Substituting the given values, we get \(SE = \frac{6}{\sqrt{39}} \approx 0.96\).
Step 2 :Calculate the z-scores for $76 and $77 using the formula \(Z = \frac{(X - \mu)}{SE}\). Substituting the given values, we get \(Z1 = \frac{(76 - 75)}{0.96} \approx 1.04\) and \(Z2 = \frac{(77 - 75)}{0.96} \approx 2.08\).
Step 3 :Look up the z-scores in the z-table to find the corresponding probabilities. We find that \(P(Z1) = 0.850\) and \(P(Z2) = 0.981\).
Step 4 :Calculate the probability that the sample mean is between $76 and $77 by subtracting the probabilities found in the previous step. We get \(P(76 < X < 77) = P(Z2) - P(Z1) = 0.981 - 0.850 = 0.131\).
Step 5 :\(\boxed{0.131}\) is the probability that the sample mean of sales per customer is between $76 and $77.