Answer:
1) mean = 21, standard deviation σ = 21.9317
2) the probability that Penelope's portfolio will earn at least 12% in the next 12 months is 0.6591
Step-by-step explanation:
Given the data in the question;
1. According to Penelope's beliefs, what are the mean rate of return and the standard deviation of return of her portfolio?
Mean μ = Return = ( 60% × 15) + ( 40% × 30 ) = 9 + 12 = 21
mean = 21
standard deviation σ = √( (0.6² × 25²) + ( 0.4² × 40² ) )
standard deviation σ = √( (0.36 × 625) + ( 0.16 × 1600 ) )
standard deviation σ = √( 225 + 256 )
standard deviation σ = √481
standard deviation σ = 21.9317
2) What is the probability that Penelope's portfolio will earn at least 12% in the next 12 months
so we are to find P( X > 12 )
converting into standard normal variable;
⇒ P( Z > X-μ / σ )
= P( Z > ( 12-21 / 21.9317 ) )
= P( Z > ( -9 / 21.9317 ) )
= P( Z > -0.41 )
FROM z-score table; P( Z > -0.41 ) is 0.3409
P( X > 12 ) = 1 - 0.3409
P( X > 12 ) = 0.6591
Therefore, the probability that Penelope's portfolio will earn at least 12% in the next 12 months is 0.6591
