00:01
By given data, we can observe that a certain mutual count has annual rate, has annual rate of return, that is approximately, that is approximately normally distributed with mean of 5%.
00:29
So we can write mean mu is equal to 5 % and standard deviation denoted by sigma is equal to 4%.
00:38
Now calculating the probability that your one area of return will be negative.
00:45
Probability that the 1 p of return will be negative is equal.
01:00
So this can be calculated as p of x less than 0.
01:05
Using the z formula we have p of z less than 0.
01:10
Minus 5 over 4 which is x minus mu over sigma this is equal to 1 .25 so p of z less than 1 .25 can be calculated from the z score table which is equal to 0 .1056 similarly we have p of x greater than 0 is equal to 1 minus 0 .1056 which is 0 .894.
01:45
This is the required probability for the first part.
01:51
Now we have the probability that your 1 year return will exceed 15 % which is denoted by p of x greater than 15 and this is equal to p of z greater than 15.
02:07
Over which is x minus mu over sigma is equal to 2 .5.
02:12
So from this we have p of z value greater than 2 .5 should be calculated from the z school table.
02:19
So p of x greater than 15 is equal to 0 .006...