I'm studying this book and on page 364 when he is starting to define confidence intervals, he made this big jump first saying the sample proportion fall within 1.96 standard deviation of the population proportion (it's natural, since the population proportion is in the center of the distribution) to just after saying the other way around, it's the population proportion that falls within 1.96 standard deviation of the sample proportion.
Why this is true? following the first sentence we should have had:
...,Then the interval from
[population proportion - 1.96(standard deviation)] to
[population proportion + 1.96(standard deviation)]
contains the sample proportion.
I need help, for me this isn't clear at all