The Bank of England Inflation Attitudes Survey asks individuals about their inflation perceptions and expectations in eight intervals including an indifference limen. This paper studies fitting a mixture normal distribution to such interval data, allowing for multiple modes. Bayesian analysis is useful since ML estimation may fail. A hierarchical prior helps to obtain a weakly informative prior. The No-U-Turn Sampler speeds up posterior simulation. Permutation invariant parameters are free from the label switching problem. The paper estimates the distributions of public inflation perceptions and expectations in the UK during 2001Q1–2017Q4. The estimated means are useful for measuring information rigidity.