Examine the probability distribution shown below. Complete parts a through d.

xP(x)

50.03

100.04

150.15

200.15

250.35

300.15

350.01

400.06

450.02

500.04

a. Calculate the expected value and standard deviation for this random variable.

E(x)=

(Type an integer or adecimal.)

_x = (Round to twodecimal places as needed.)

b. Denote the expected value as

- =(Round to twodecimal places as needed.)

+ =(Round to twodecimal places as needed.)

c. Determine the proportion of the distribution that is contained with the interval

(Type an integer or adecimal.)

d. Repeat part c for (1) 2 and (2) 3

(1) Determine the proportion of the distribution that is contained within the interval 2.

(Type an integer or adecimal.)

(2) Determine the proportion of the distribution that is contained within the interval ) 3.

(Type an integer or adecimal.)