Let the random variable \(X\) represent the number of adults wearing a watch on their left wrist. Given that 76% wear a watch on their left wrist, \(X\) follows a binomial distribution \(B(n=200, p=0.76)\).

We approximate this binomial distribution with a normal distribution. The mean \(\mu\) and variance \(\sigma^2\) are calculated as follows:

\(\mu = np = 200 \times 0.76 = 152\)

\(\sigma^2 = np(1-p) = 200 \times 0.76 \times 0.24 = 36.48\)

We use a continuity correction to find \(P(X > 155)\), which is approximated by \(P(X > 155.5)\) in the normal distribution.

Standardizing, we have:

\(Z = \frac{155.5 - 152}{\sqrt{36.48}} = \frac{3.5}{6.036} \approx 0.5795\)

Thus, \(P(X > 155) = 1 - \Phi(0.5795) \approx 1 - 0.7188 = 0.281\).