Question

On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below.

x   0 1 2 3 4 5 Total

P(x) .05 .44 .30 .17 .03 .01 1.00

(a) Calculate the mean and standard deviation. (Round your mean value to 2 decimal places and standard deviation to 3 decimal places.)

a. Mean

b. Standard deviation

(b) Describe the shape of this distribution:

a. Skewed to the right

b. Skewed to the left

c. Symmetric

Answer 1

(a)

x	p	xp	x2p
0	0.05	0	0
1	0.44	0.44	0.44
2	0.30	0.60	1.20
3	0.17	0.51	1.53
4	0.03	0.12	0.48
5	0.01	0.05	0.25
Total =	1.00	1.72	3.90

(a)

Mean = E(X) =

So,

Mean is:

1.72

(b)

Variance s² is given by:

So,

Standard deviation is given by:

s =

So,

Standard deviation is given by:

0.9704

(c)

Correct option:

a. Skewed to the right