91Ó°ÊÓ

Given in the question that, In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame can be adjusted to one of five different settings. Here is the probability distribution of the flame temperature $X$(in degrees Celsius) for a randomly chosen glass:

We need to find the mean and standard deviation of the number of degrees off target,$D=X−550$, if the target temperature is $550°C$.

The probability distribution is:

The equation is:

$D=X-550$

Mean and standard deviation are:

${\mathrm{μ}}_X=550$

${\mathrm{σ}}_X=5.7$

The mean and standard deviation can be calculated as:

${\mathrm{μ}}_{X−550}={\mathrm{μ}}_X−550$

$=550−550$

$=0$
${\mathrm{σ}}_{X−550}={\mathrm{σ}}_X$

$=5.7$

The mean and standard deviation are $0$and $5.7$.

In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame can be adjusted to one of five different settings. Here is the probability distribution of the flame temperature $X$(in degrees Celsius) for a randomly chosen glass:

We need to find the mean $\mathrm{μ}Y$and the standard deviation $\mathrm{σ}Y$of the temperature of the flame

The mean and standard deviation can be calculated as:

${\mathrm{μ}}_{\frac{9}{5}X+32}=\frac{9}{5}{\mathrm{μ}}_X+32$

$=\frac{9}{5}\left(550\right)+32$

$={100}^{∘}\mathrm{F}$

${\mathrm{σ}}_{\frac{9}{5}}X+32=\frac{9}{5}{\mathrm{σ}}_X$

$=\frac{9}{5}\left(5.7\right)$

$={10.26}^{∘}\mathrm{F}$.