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A bag contains 30 white balls and 10 red...

A bag contains 30 white balls and 10 red balls, 16 balls are drawn on by one randomly from the bag with replacement. If X is the number of white balls drawn, then
`(("mean of X")/("standard deviation of X"))` is equal to

A

`(4sqrt(3))/(3)`

B

4

C

`3sqrt(2)`

D

`4 sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Number of white balls `=30`
and number of red balls `=10`
Let p = probability of success in a trial = probability of getting a white ball in a trial `=(30)/(40)=(3)/(4).`
and q = probability of failure in a trial
` =1-p=1-(3)/(4)=(1)/(4)`
Here,n = number of trials = 16.
Clearly, X follows binomial distribution with parameter `n= 16 and p =(3)/(4).`
`therefore " Mean of " X=np, =16.(3)/(4)=12`
and variance of `X=npq=16.(3)/(4).(1)/(4)=3`
Now, `("mean of X")/("standard deviation of X")=(12)/(sqrt(3))=4 sqrt(3) " " [ because SD=sqrt("variance")]`
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