Define the term "combined standard uncertainty" and "coverage interval".

The effective diameter of a screw thread is determined by the three wire method as $E=W-d(cosec+1)+$

$(\frac{p}{2})cot,$ where $W$ is the diameter over wires, $d$ is the diameter of the wire used, $p$ the pitch of the

screw and $$ the angle of the thread. The diameter over wires was measured repeatedly with the readings

$23\mathrm{.}1,23\mathrm{.}222\mathrm{.}9,23\mathrm{.}2$ and $22\mathrm{.}8$ mm $.$ The diameter of the wire was measured as $1\mathrm{.}48$ mm using a digital

micrometer of least count $0^{}\mathrm{.}01mm$ and repeated readings did not show any variation. The thread angle

was measured using a microscope as $60$ with uncertainty triangularly distributed between $\frac{+}{-}0\mathrm{.}5.$ The

pitch of the thread was found using a thread pitch gauge and the error is not expected to exceed $0\mathrm{.}05$

mm $.$ Determine the effective diameter of the thread and its $90\%$ lower and upper coverage intervals.

$($Neat uncertainty budget table $1\mathrm{.}0+$ std uncs $2\mathrm{.}0+$ sensitivities$/$contribs $4\mathrm{.}0+$ combined $0\mathrm{.}5+$edgh$+t$ bor

factor $0\mathrm{.}5+Cl1=10$ marks$)$

Hundred sheets of paper are used to make a stack. The thickness of the paper is known to be $0\mathrm{.}1$ mm with

standard uncertainty $0\mathrm{.}02$ mm $.$ Determine the height of the stack and its standard uncertainty.

A circuit consists of three resistances connected in series. The resistances were measured using a digital

multimeter as $20,30$ and $50$ ohms. Deternine the standard uncertainty in the circuit, if the standard uncertainty in

the resistances were $1,2$ and $3$ ohms respectively and all the resistance measurements had a correlation coefficient

of $0\mathrm{.}6$ between them.

the average height of a gauge block was found to be $48\mathrm{.}1325$ mm with standard uncertainty $0\mathrm{.}0263$ mm $.$ How

will you report the result according to the GUM guidelines?

The diameter of a cheap washer is specified is $12\mathrm{.}0-0\mathrm{.}1mm.$ A sample washer was measured as $11\mathrm{.}99+1-0\mathrm{.}02$

$mm(95\%).$ Determine if the bullet is acceptable with guard band a$)100\%,$ b$)50\%.$ Give reasons with sketch.