Question

Suppose that over a certain period, the percent change in the daily adjusted close of the S&P500 can be approximately modeled as a normal random variable with mean 0.04% and standard deviation 0.92%.

a) What is the probability that on a randomly selected day the change is between -1.3% and +1.7%?

b) On how many of 100 randomly selected days in this period would a change above +2.0% would be expected?

c) What is the 85th percentile of this variable?

show all work please not just excel formula

Answer 1

Х~( 0-0ч, 2-4 2*) а) Р (-13 LX2 1-1) що и standard normal and a dish cho table. Р[ 2 21:1 – 0-0ч) - Р/ 2 2 - 1-3- р -оч 2.4 0-9 - P(ta 1:80) - P( 2 2-1ч6) = P(tel-90) - Lt- P( eet-41) Ә) P ( 221-80) + P ( -ч) – 1 = - о - 96 91 + 0,0219-12 0,492. P( x; 2) P( 2 2 2 - 1 P(t22-13) = t - P(22-13) 2-4 - 1 - 0 9 34 2 0 -04 66 з і 4 10% - 100x 0 - 0 1 6 6 2 1-66 у что 85th percentiles Ф/2.— Т. = P2 a scose corresponding 19 О- val used z table (5) 2 ) (1) 2 - о- оч :0364 3 2 2-o-92-xt-03643 +0-09 0:44 2 - 94 35 (3rdP)