Answer to Question #238431 in Statistics and Probability for baber

Question

) A random sample of seventy two six funds averages a 13.9 per cent annual investment return for 2001–2 with a standard deviation of 4.6 per cent annual return. The BSE Stock Index grew at an annual average rate of 27.3 per cent over the same period. Do these data show that, on the average, the mutual funds out-performed the BSE Stock Index during this period?

Answer 1

Let x be the number of students who have done their homework

Given Population(N)= 20 ; Sample(n)=4 ; done homework (m)= m

Then the proof of x is

$P(x=k)= \frac{\begin{pmatrix} m \\ k \end{pmatrix} \begin{pmatrix} N-m \\ n-k \end{pmatrix}}{\begin{pmatrix} N \\ n \end{pmatrix}}= \frac{\begin{pmatrix} 15 \\ k \end{pmatrix} \begin{pmatrix} 20-m \\ 4-k \end{pmatrix}}{\begin{pmatrix} 20 \\ 4 \end{pmatrix}}$

P( exactly 3 will have done their work)

$= P(x=3)\\ = \frac{\begin{pmatrix} 15 \\ 3 \end{pmatrix} \begin{pmatrix} 20-15 \\ 4-3 \end{pmatrix}}{\begin{pmatrix} 20 \\ 4 \end{pmatrix}}\\ = \frac{(\frac{15!}{(15-3)! 3!}) (\frac{5!}{(5-1)! 1!})}{(\frac{20!}{(20-4)! 4!})}\\ =\frac{455*5}{4845}\\ =0.47$

NO, these data do not show that, on average, the mutual funds outperformed the BSE Stock Index during this period. The standard deviation (represented by the symbol sigma, ) indicates the amount of variation or dispersion from the average (mean) or expected value. It is, more specifically, a measure of the average distance between the data values in the collection and the mean.

The BSE Stock Index grew at an annual average rate of 27.3 percent over the same period while the annual investment return for 2001–2 had a standard deviation of 4.6 percent annual return