Question

The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20,0.25,0.20, 0.20, respectively.

43.) What is the mean that a surgeon operates on patients in any one day?

 a. 5.0             b. 5.1              c. 5.2              d. 5.3              e. 5.4

44.) What is the variance of the given problem?

 a. 1.76           b.1.77             c. 1.78            d. 1.79            e. 1.80

45.) What is the standard deviation of the given problem?

 a. 1.33           b. 1.35            c. 1.37            d. 1.36            e. 1.34

Answer 1

The mean of a discrete random variable X:

$\mu=\Sigma XP(X).$

The variance of a discrete random variable X:

$\sigma^2=\Sigma (X-\mu)^2 P(X).$

The standard deviation of a discrete random variable X:

$\sigma=\sqrt{\sigma^2}=\sqrt{\Sigma (X-\mu)^2 P(X)}.$

To simplify calculations we can use the table:

So we can find out the mean:

$\mu=\Sigma XP(X)=0.45+0.80+1.25+1.20+1.40=5.10=5.1$ (43. b)

To find the variance we have to continue calculations:

We can find the variance now:

$\sigma^2=\Sigma (X-\mu)^2 P(X)=0.6615+0.2420+0.0025+0.1620+0.7220=1.79$ (44. d)

And the last step, the standard deviation:

$\sigma=\sqrt{\sigma^2}\approx 1.34$ (45. e)

Answer: 43. b 44. d 45. e