The proportion of observation that lies between \(46\) and \(54\) is \(68\%\).
What is empirical rule ?
Empirical rule : In statistics, the \(68-95-99.7\) rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: \(68\%,\) of the values lie within one standard deviations of the mean.
i.e. \(\mu -\sigma\) and \(\mu+\sigma\)
We have,
Mean \((\mu)=50\)
Standard deviation \((\sigma)=50\)
So,
Now Using the Empirical rule,
\(\mu -\sigma\) and \(\mu+\sigma\)
i.e.
\(50-4=46\)
and, \(50+4=54\)
That means,
That data lie between \(46\) and \(54\) is \(68\%\).
Hence, we can say that the proportion of observation that lies between \(46\) and \(54\) is \(68\%\).
To know more about Empirical rule click here
https://brainly.com/question/14728973
#SPJ3
