At the end of Section 8.3, it was noted that for samples of serum cholesterol
levels of size 25—-drawn from a population with mean µ = 211 mg/ 100 ml and
standard deviation σ = 46 mg/100 ml—-the probability that a sample mean
x lies within the interval (193.0, 229.0) is 0.95. Furthermore, the probability that the mean
lies below 226.1 mg/100 ml is 0.95, and the probability that it is above 195.9 mg/100
ml is 0.95. For all three of these events to happen simultaneously, the sample mean
x would have to lie in the interval (195.9, 226.1). What is the probability that this
occurs?
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