We model the chemotaxis signaling pathway of E.coli, and simulate swimming trajectories for large populations. Additive noise in the signaling pathway leads to Lévy walk-like behavior in absence of chemical gradients, which represents an optimal search strategy to find randomly located and sparse nutrients. We derive the power-law run length distribution, characteristic for a Lévy-walk, from relations given by the signaling pathway, and investigate the influence of noise on bacterial chemotaxis and chemotactic pattern formation. Signaling noise leads to higher bacterial motility and increased behavioral variability, but reduces chemotactic precision. Aggregate formation is strongly influenced by population and domain size, and signaling noise affects the shape of the aggregates.