Home
Class 12
MATHS
Let a random variable X have a binomial ...

Let a random variable X have a binomial distribution with mean 8 and variance r. If `P(X le 2 ) = (k)/(2^(16))`, then k is equal to

A

17

B

121

C

1

D

137

Text Solution

Verified by Experts

The correct Answer is:
D
Let for the given random variable 'X' the binomial probability distribution have n-number of independent trials and probability of success and failure are p and q respectively. According to the question,
Mean =np =8 and variance=npq=4
`:. Q=(1)/(2)rArr p=1-q=(1)/(2)` Now, `nxx(1)/(2)=8rArr n=16`
`P(X=r)=^(16)C_(r )((1)/(2))^(16)`
`:. P(X le 2)=P(X=0)+P(X=1)+P(X=2)`
`=^(16)C_(0)((1)/(2))^(16)+overset(16)""C_(1)((1)/(2))^(16)+overset(16)""C_(2)((1)/(2))^(16)`
`=(1+16)+120)/(2^(16))=(137)/(2^(16))=(k)/(2^(16)) " "` (given)
`rArr " "k=137`
Promotional Banner

Similar Questions

Explore conceptually related problems

In a binomial distribution with mean 4 and variance 16/5 then p is

For a binomial distrubution with mean 2 and variance 4/3 p is equal to

Let X have a Bernoulli distribution with mean 0.4, then the variance of (2X-3) is

A random variable X has binomial distribution with n=36 and p =0.8 then standard deviation of x is

If X is a random variable with the following distribution then k is

A random variable X has binominal distribution with n = 25 and p = 0.8 then standard deviation of X is

A random variable X has binomial distribution with n=25 and p=0.8 then standard deviation of X is ……………..

In a Binomial distribution if n = 5 and P(X=3) =2P (X=2) find p.