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

x P(x) 5 0.02 10 0.06 15 0.14 20 0.15 25 0.35 30 0.10 35 0.08 40 0.05 45 0.02 50 0.03

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

E(x)=

(Type an integer or a decimal.)

Part 2

x=

(Round to two decimal places as needed.)

Part 3

b. Denote the expected value as . Calculate and +.

=

(Round to two decimal places as needed.)

Part 4

+=

(Round to two decimal places as needed.)

Part 5

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

(Type an integer or a decimal.)

Part 6

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 a decimal.)

Part 7

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

3.

(Type an integer or a decimal.)