91影视

Given :

$X$: Resistance of a 100-ohm resistor

$Y$: Resistance of a 250 -ohm resistor

Mean,

${渭}_X=100$ohms

${渭}_Y=250$ohms

Standard deviation,

${蟽}_X=2.5$ohms

${蟽}_Y=2.8$ohms

The two components in series are $\mathrm{X}\mathrm{and}\mathrm{Y}.$

As a result, the total resistance of two components in series is $X+Y$.

A normal distribution exists for both $\mathrm{X}\mathrm{and}\mathrm{Y}$.

As a result, $X+Y$has a normal distribution as well.

If $\mathrm{X}\mathrm{and}\mathrm{Y}$ are unrelated, Property mean :

${渭}_{aX+bY}=a{渭}_X+b{渭}_Y$

Property variance : ${{蟽}^2}_{aX+bY}=a^2{渭}_X+b^2{渭}_Y$

As a result, Total resistance average :

$$\begin{gathered} {渭}_{X+Y}={渭}_X+{渭}_Y \\ =100+250 \\ =350\mathrm{ohms} \end{gathered}$$

Total resistance variation :

$$\begin{gathered} {{蟽}^2}_{x+y}={{蟽}^2}_X+{{蟽}^2}_Y \\ ={(2.5)}^2+{(2.8)}^2 \\ =\mathbf{14}\mathbf{.}\mathbf{09}\mathrm{ohms} \end{gathered}$$

We know that the square root of the variance is the standard deviation.

The standard deviation of total resistance $X+Y$:

$$\begin{gathered} {蟽}_{x+y}=\sqrt{{{蟽}^2}_X+{{蟽}^2}_Y} \\ =\sqrt{14.09} \\ 鈮�\mathbf{3}\mathbf{.}\mathbf{7537}ohms \end{gathered}$$

Given :

$X$: Resistance of a $100-$ohm resistor

$Y$: Resistance of a $250-$ohm resistor

Mean,

${渭}_X=100$ohms

${渭}_Y=250$ohms

Standard deviation,

${蟽}_X=2.5$ohms

${蟽}_Y=2.8$ohms

Calculate the $z-$score using the formula

$$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{345-350}{3.7537} \\ 鈮�-1.33 \end{gathered}$$

Or

$$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{350-345}{3.7537} \\ 鈮�1.33 \end{gathered}$$

To find the equivalent probability, use the normal probability table in the appendix. In the typical normal probability table for $P(Z<-1.33)$, look for the row that starts with $-1.3$and the column that starts with $.03$.

Or In the typical normal probability table for $P(Z<1.33)$, look for the row that starts with $1.3$and the column that starts with $.03$.

$$\begin{gathered} P(345<X+Y<355)=P(-1.33<z<1.33) \\ =P(Z<1.33)-P(Z<-1.33) \\ =0.9082-0.0918 \\ =\mathbf{0}\mathbf{.}\mathbf{8164} \end{gathered}$$