probability of interval
This is the problem I am working on- The weights X of eggs produced at a particular farm are normally distributed with mean 1.72 ounces and
standard deviation 0.12 ounce. Eggs whose weights lie in the middle 75% of the distribution of weights of
all eggs are classified as “medium.” Find the maximum and minimum weights of such eggs. (These weights
are endpoints of an interval that is symmetric about the mean and in which the weights of 75% of the
eggs produced at this farm lie.)
However, I am confused as to how should I know where this range begins and ends. How do I calculate that before I begin?Pleasae show steps. Thanks
+33665 The middle 75% means the upper and lower limits are at the points 87.5% and 12.5% respectively (i.e. 25% in total beyond these limits).
You need to know that these limits are approximately 1.15 standard deviations away from the mean (use an online Normal distribution calculator [e.g. http://stattrek.com/online-calculator/normal.aspx ] or look up in tables or use another piece of software with normal distribution calculations [e.g. Excel] to find this).
So, upper limit weight $${\mathtt{1.72}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1.15}}{\mathtt{\,\times\,}}{\mathtt{0.12}} = {\frac{{\mathtt{929}}}{{\mathtt{500}}}} = {\mathtt{1.858}}$$ ounces
Lower limit weight $${\mathtt{1.72}}{\mathtt{\,-\,}}{\mathtt{1.15}}{\mathtt{\,\times\,}}{\mathtt{0.12}} = {\frac{{\mathtt{791}}}{{\mathtt{500}}}} = {\mathtt{1.582}}$$ ounces
