It is suspected that a random variable has a normal distribution with a mean of 6 and a standard deviation of 0.5. After observing several hundred values, we find that the mean is approximately equal to 6 and the standard deviation is close to 0.5. However, we find that 53% percent of the observations are between 5.5 and 6.5 and 83% are between 5.0 and 6.0. Does this evidence increase or decrease your confidence that the data are normally distributed?

Explain your answer.