A machine is set to produce bolts of nominal diameter $25-0 \mathrm{~mm}$. Measurement of the diameters of 60 bolts gave the following frequency distribution:
\begin{tabular}{|l|c|c|c|c|}
\hline Diameter $x(\mathrm{~mm})$ & $23 \cdot 3-23 \cdot 7$ & $23-8-24 \cdot 2$ & $24 \cdot 3-24-7$ & $24 \cdot 8-25-2$ \\
\hline Frequency $f$ & 2 & 4 & 10 & 17 \\
\hline
\end{tabular}
\begin{tabular}{|l|c|c|c|}
\hline Diameter $x(\mathrm{~mm})$ & $25-3-25-7$ & $25-8-26-2$ & $26 \cdot 3-26-7$ \\
\hline Frequency $f$ & 16 & 8 & 3 \\
\hline
\end{tabular}
(a) Calculate (i) the mean diameter and (ii) the standard deviation from the mean.
(b) For a full run of 3000 , calculate (i) the limits between which all the diameters are likely to lle, (ii) the number of bolts with diameters less than $24.45 \mathrm{~mm}$.