At the end of section 8.3, it was noted that for samples of serum

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?