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2. Over the past five years, a stock produced returns of 14%, 22%, -16%, 4%, and 11%. If the returns are normally distributed

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Answer #1

Average \:return (m) = \frac{14 + 22 - 16 + 4 +11}{5}

m = 7

Returns (X) X- m (X-m)2
14 7 49
22 15

225
-16 -23 529
4 -3 9
11 4 16

S.d = \sqrt{\frac{\sum{(X- m)^{2}}}{n-1} }

= \sqrt{828 /4}

= 14.387 = 14.4 (approx)

Mean - Lower limit = 7 - (-7.4) = 14.4

Upper limit - Mean = 21.4 - 7 = 14.4

As the range is one standard deviation away from mean on both the sides

Using standard deviation and coverage properties, about 68.27% of values drawn from a normal distribution are within one standard deviation σ away from the mean.

Hence, the required probability is 68.27%.

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