Answer:
Therefore the required probability is 0.83427.
Step-by-step explanation:
Binomial (n,p) distribution:
A discrete random variable X having the set {0,1,2,3.....,n} as the spectrum, is said to have binomial distribution with parameter n=the number of trial in the binomial experiment,p= the probability of success on an individual trial, if the probability mass function of X is given by
[tex]P(X=x)=^nC_x p^x(1-p)^{n-x}[/tex] for x= 0,1,2,....
=0 elsewhere
where n is a positive integer and 0<p<1.
[tex]^nC_x=\frac{n!}{r!(n-r)!}[/tex]
Given that,
n= 9 and p=0.25
We are interested to find P(x<4).
P(x<4)
=P(x=0)+P(x=1)P(x=2)+P(x=3)
[tex]=^9C_0 (0.25)^0(1-0.25)^{9-0}+^9C_1 (0.25)^1(1-0.25)^{9-1}+^9C_2 (0.25)^2(1-0.25)^{9-2}+^9C_3 (0.25)^3(1-0.25)^{9-3}[/tex]
[tex]=\{1\times 1\times (0.75)^9\}+\{9\times 0.25\times (0.75)^8\}+\{36 \times (0.25)^2\times (0.75)^7\}+\{84\times (0.25)^3\times (0.75)^6\}[/tex]
≈ 0.83427
Therefore the required probability is 0.83427.
