Since there is a noticeable skewness to the right, we will get a poor approximation of areas if we replace the rectangles by a normal curve. If the value of p were .90 instead of .10, the binomial histogram would be skewed left. This is typical behavior of binomial histograms whenever p is either too close to 0 or too close to 1. When is it 'safe' to use the normal curve to approximate binomial probabilities? A convenient rule of thumb is as follows:
The reader is reminded that normal curve approximations, no matter how close, are still approximations. The binomial formula ( 4.3) should be used to calculate exact probabilities whenever possible.