[See Steps] Determine the price range (in 6 months) for the stock at 95% confidence intervals. Probability theory suggests, for a normally distributed random
Question: Determine the price range (in 6 months) for the stock at 95% confidence intervals.
Probability theory suggests, for a normally distributed random variable, about 95 % of sample occurrences should be within the range of 1.96 standard deviations from the mean value 1 .
Therefore, 95% confidence intervals for ln S T are
Lower bound: 3.759 – (1.96)(0.141) =
Upper bound: 3.759 + (1.96)(0.141) =
In other words, 3.4826 < ln S T < 4.0354.
Notice that these boundaries are in logarithms forms. To convert them back to dollars and cents, you need to take the antilogarithms. 2
That is, \[{{e}^{3.4826}}<{{e}^{\ln {{S}_{T}}}}<{{e}^{4.0354}}\] .
And the answer is $32.5454 < S T < $56.5633 .
A Standard Normal Distribution
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