A report gives only a 95% interval for the share of shoppers who use a loyalty card: from 0.38 to…

Step 1. Midpoint. $\dfrac{0.38 + 0.46}{2} = 0.42$.

Step 2. Half the width. $\dfrac{0.46 - 0.38}{2} = 0.04$.

Step 3. The size. $n = \left(\dfrac{1.96}{0.04}\right)^2 \times 0.42 \times 0.58 = 2401 \times 0.2436 \approx 584.9$, so about $585$ shoppers.