Question

The stock market moves up 0.03% on the average with a standard deviation of 0.92%. What is the probability of the market dropping -5% or more on the next trading day? Convert the answer to a percentage and round to the tenth.

Answer 1

The stock market moves up 0.03% on the average with a standard deviation of 0.92%.

Let X be stock market movement the X~ $N(\mu=0.03,\sigma^2=0.92^2)$

We have to find P(X<-5)

We will normalize X by sbtracting $\mu=0.03$ and dividing by$\sigma=0.92$ on both sides

P(x<-5)=$P(\frac{X-0.03}{0.92}<\frac{-5-0.03}{0.92})=P(Z<-5.47)$

Here Z~N(0,1)

Hence P(X<-5)=P(Z<-5.47)=0 (Using normal probability tables we have P(Z<-5.47)=0

Probability of the market dropping -5% or more on the next trading day is 0 percent