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:

$\sigma_{\mu p}=\sqrt[\placeholder{⬚}]{\frac{p*q}{n}}$

Where q is equal to:

q=1-p.

Substituing:

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

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

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

$\begin{gathered} Z=\frac{x-\mu_p}{\sigma_{\mu p}} \\ \\ Z=\frac{0.44-0.4}{0.02}=2 \end{gathered}$

fOR Z= 2, P(Z)=0.9772

Therefore,

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