The probability distribution for the rate of return on an investment is

Rate of Return
(In Percent) Probability
9.5 .1
9.8 .2
10.0 .3
10.2 .3
10.6 .1

a. What is the probability that the rate of return will be at least 10%?
b. What is the expected rate of return?
c. What is the variance of the rate of return?

a)0.7

b) 10.03

c)  0.0801

Step-by-step explanation:

Rate of return   Probability

9.5                           0.1

9.8                           0.2

10                             0.3

10.2                          0.3

10.6                          0.1

a.

P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)

P(Rate of return is at least 10%)=0.3+0.3+0.1

P(Rate of return is at least 10%)=0.7

b)

Expected rate of return=E(x)=sum(x*p(x))

Rate of return(x)   Probability(p(x))    x*p(x)

9.5                           0.1                       0.95

9.8                           0.2                      1.96

10                             0.3                        3

10.2                          0.3                        3.06

10.6                          0.1                       1.06

Expected rate of return=E(x)=sum(x*p(x))

Expected rate of return=0.95+1.96+3+3.06+1.06=10.03

c)

variance of the rate of return=V(x)=

Rate of return(x)   Probability(p(x))    x*p(x)    x²*p(x)

9.5                           0.1                       0.95       9.025

9.8                           0.2                      1.96         19.208

10                             0.3                       3             30

10.2                          0.3                       3.06        31.212

10.6                          0.1                       1.06         11.236

sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681

variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²

variance of the rate of return=V(x)=100.681-(10.03)²

variance of the rate of return=V(x)=100.681-100.6009

variance of the rate of return=V(x)=0.0801

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west