Question

Calculate the standard deviation if a total of 52 beads are drawn and the probability of drawing a white bead is 0.34 and the probability of drawing a red bead is 0.66.

Answer 1

Answer: 3.416

Step-by-step explanation:

Let Event R = drawing a red bead

Event W = drawing a white bead

As per given : P(R) = 0.66 and P(W)=0.34

Also, P(R)+P(W)=0.66+0.34=1.00

It means , there are only two events.

In Binomial distribution (For two independent event) , the standard deviation is given by :-

$\sigma=\sqrt{npq}$ , where n= number of trials , p = probability of getting one event , q = probability of getting other event.

For current situation , n= 52 , p=0.66 , q=0.34

Substitute the corresponding values  , we get

$\sigma=\sqrt{52(0.66)(0.34)}$

$\sigma=\sqrt{11.6688}$

$\sigma=3.41596252907\approx3.416$

Hence, the standard deviation is 3.416.