Please show work! 7. Normal Distribution Aftcr Faccbook\'s carnings announccment
ID: 3041639 • Letter: P
Question
Please show work!
7. Normal Distribution Aftcr Faccbook's carnings announccment wc havc thc following distribution of rcturns. First, thc stock beats earnings expectations 75% of the time, and the other 25% of the time earnings are in line or disappoint. Second, when the stock beats earnings, the probability distribution of percent changes is normal with a mean of IC% with a standard deviation of 5% and, when the stock misses earnings, a normal with a mean of 5% and a standard deviation of 8%, respectively (a) Ahead of the earnings announcement, what is the probability that Facebook stock will have a return greater than 5%? (b) Do you get the same answer for the probability that it drops at least 5%?Explanation / Answer
Mean = 0.75*10-0.25*5 = 6.25%
Standard deviaton = sqrt( 0.75*5^2 +0.25*8^2) = 5.894%
Z = (x-mean)/sigma = (5-6.25)/5.894 = -0.212
P(z>-0.212) = 1-0.416054= 0.583946
Z2 = (-5-6.25)/5.894=-1.908
P(Z<-1.908) = 0.028196 from Z tables