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.

Question

asked Feb 3, 2021 27.0k views

1 Answer

Shaunice · Answer 1 · 2021-02-09T07:18:03+0000

Answer: 3.416

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 :-

$\sigma=√(npq)$ , 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

$\sigma=√(52(0.66)(0.34))$

$\sigma=√(11.6688)$

$\sigma=3.41596252907\approx3.416$

Hence, the standard deviation is 3.416.