The return on a mutual fund has a normal distribution with expected value of 15% and standard deviation of 22%. The NAV of the mutual fund is $40. The fund is expected to distribute $2 in dividend to its shareholders one year from now. Calculate the probability that the NAV of the mutual fund a year from now (after the dividend distribution) will be between $50 and $60?
Since the return of MF is following Normal distribution curve ,
So the problem can be solved by use of Z score =
Required NAV before dividend distribution = $50+2 =$52 and $ 60+2 = $62 ,
Return % = 52-40/40 = 30% and 62-40/40 =55%
Assume , dividend distribution tax is ZERO( as not given in question )
Z -Score52 = 30 -15 /22 = 0.6818 and Z -Score62 = 55 -15 /22 = 1.8182
After getting the value in Z-table
Z -Score52 = 0.7517 Z -Score62 = 0.9649
Area in between = 0.9649 - 0.7517 = 0.2132
Probability for required NAV = 21.32%
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