Posted by Jennifer on Friday, November 11, 2011 at 1:19pm.
Answer the following:
(A) Find the binomial probability P(x = 4), where n = 12 and p = 0.30.
(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? Please show how you would calculate ยต and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.

MATH  latoya, Saturday, December 10, 2011 at 2:29am
=0.2311
(B) p(x is at most 4)=P (x,=4)=p(0)+p(1)+p(2)+p(3)+p(4)
=c(12,0)(0.30)^0(10.30)^2(120)+c(12,1)(0.30)^1(10.30)^(121)
+c(12,2)(0.30)^2(10.30)^(122)+c(12,3)(0.30)^3(10.30)^(123)+c(12,4)(0.30)^4(10.30)^(124)
(C) u=np=12*0.3=3.6
12*0.3*0.7=2.52
(2.52)=1.5875
to find p(4), we applies the continuity correction factor and find p(3.5<x<4.5). this because using the normal distribution p(x=4) will be 0.
z=(3.43.6)/1.5875=0.0630and z=(4.53.6)/1.5875=0.5669
P(4)= P(3.5<x<4.5)=P(0.063<z<0.5669)=0.2397