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Given in the question that, Knees Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of $1$(low) to $5$(high). Let $X$be the pain score for a randomly selected patient.

We need to find $P(X=5)$

Given:

the probability distribution is

The formulas to compute the mean and standard deviation are:

localid="1649746524407" $蟽=\sqrt{鈭�x^2脳P\left(x\right)鈭�{\left(鈭�x脳P\left(x\right)\right)}^2}$

Let localid="1649746530834" $\mathrm{x}$be the missing value.

The missing value can be calculated as:

localid="1649746539988" $0.1+0.2+0.3+0.3+x=1$

localid="1649746546770" $x+0.9=1$

localid="1649746553075" $x=0.1$

localid="1649746559408" $P(X=5)$can be calculated as:

localid="1649746565386" $P(X=5)=x$

localid="1649746571448" $=0.1$

Given in the question that, Knees Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of $1$(low) to $5$(high). Let$X$be the pain score for a randomly selected patient.

We need to find the probability that both of the patients scores either $1$or $2$

The probability that both of the patients scores either$1$or $2$is computed as:

$P\left(1\text{or}2\right)=P(X=1)+P(X=2)$

$=0.1+0.2$

$=0.3$

The probability that both of the patients scores either$1$or $2$is computed as:

$P(1$or $2$$)=P(1$or $2$$)脳P(1$or $2)$$)$

$=0.3脳0.3$

$=0.09$

Knees Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of $1$(low) to $5$(high). Let $X$be the pain score for a randomly selected patient.

We need to compute the mean and standard deviation of X .

The mean can be calculated as:

$\mathrm{Mean}=鈭�x脳P\left(x\right)$

$=1\left(0.1\right)+2\left(0.2\right)+3\left(0.3\right)+4\left(0.3\right)+5\left(0.1\right)$

localid="1649746701130" $=3.1$

The standard deviation is calculated as follows:

localid="1649746705865" $蟽=\sqrt{鈭�x^2脳P\left(x\right)鈭�{\left(鈭�x脳P\left(x\right)\right)}^2}$

localid="1649746709064" $=\sqrt{1^2脳0.1+2^2脳0.2+鈥�.+5^2脳0.2鈭�(3.1{)}^2}$

localid="1649746712012" $=1.1358$