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Expected monthly price change=E(x) = 0.60% Average monthly volatility = 9.40%

I am looking for the probability that gold will decline by more than 9% in the next month.

According to the formula for z score: X - E(X) / σ the equation would be= 9%-0.60% / 9.40%

Which is = .8936 which on the z score table is .3133

Since Z is positive, the probability would be 0.5 - .3133 = 0.1867 meaning that the probability of gold declining by more than 9% would be 18.67% but this is not shown on the multiple select.

A. 15.39% B. 85% C. 10.22% d. 22.36%

Mhuncho
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  • A decline of more than 9 percent is expressed via $P(X \leq -9 )$. – Keine_Maschine Sep 24 '23 at 16:58
  • Hi thanks for the comment.

    How would that be expressed as a formula ?

    -9%-o.60%/9.40% ?

     – Mhuncho Sep 24 '23 at 17:22
  • From your usage of the transformation to standard normal distribution it's clear that you didn't understand it correctly. The price change of gold is the random variable $X$, which is normal (not standard normal) distributed. To calculate the wanted probability you need to transform $X$ to a standard normal distributed random variable $Z$ correctly. Than you can use a Z-table to just read of the probability, exactly as you did in your approach. – Keine_Maschine Sep 24 '23 at 18:27
  • Thank you so much – Mhuncho Sep 24 '23 at 22:08

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