Question

Empirical research on stock market data indicates that over the course of a year, 40% of stocks go up.A random sample of 600 stocks is going to be chosen at the beginning of next year. Let p be the proportion of the stocks in the sample that go up over the course of a year.

Answer 1

Given:

probability=40%

sample=600

Mean of p:

`\mu_p=0.4`

Standar desviation:

`\sigma_(\mu p)=\sqrt[\placeholder{⬚}]{(p*q)/(n)}`

Where q is equal to:

q=1-p.

Substituing:

`\sigma_(\mu p)=\sqrt[\placeholder{⬚}]{(0.4(1-0.4))/(600)}=0.02`

Approximation for: P(p<0.44), four decimals.

We are going to find de probability finding the z-value.

`\begin{gathered} Z=(x-\mu_p)/(\sigma_(\mu p)) \\ \\ Z=(0.44-0.4)/(0.02)=2 \end{gathered}`

fOR Z= 2, P(Z)=0.9772

Therefore,

`\begin{gathered} P(\mu_p\leq0.44)=p(Z) \\ p(2)=0.9772 \end{gathered}`