Let #X# be a binomial random variable with #p=0.3# and #n=15#. What is #P(5≤X≤10)#?

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Answer 1 · 2018-01-11T11:06:20

The answer is #=0.4838#

The binomial distribution for #B(n,p)# for a random variable #X# is

#P(X=k)= ((n),(k))p^k(1-p)^(n-k)#

Here,

#B(15,0.3)#

Therefore,

#P(5<=X <=10)=sum_(k=5)^10((15),(k))p^k(1-p)^(15-k)#

From the tables,

#P(5<=X <=10)=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)#

#=0.2061+0.1472+0.0811+0.0348+0.0116+0.0030#

#=0.4838#