SOLUTION: Could someone show me how to answer these? If x is a binomial variable with p = .4 and n = 25, write the probability that you would be looking for after you have applied the co

Question 1075367: Could someone show me how to answer these?
If x is a binomial variable with p = .4 and n = 25, write the probability that you would be looking for after you have applied the continuity correction factor for the following conditions for x:
3) x = 5
4) x > 5
5) x ≤ 5

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=5; probability is 25C5(0.4)^5*0.6^20=0.0199. This is exact.
with continuity correction factor
use 4.5 and 5.5 ; mean is np=10; variance is np(1-p)=6; sd = sqrt (6). This is the normal distribution which is continuous, but we have a discrete distribution. For a specific value, we use z on each side of the integer, from the half below to the half above, since the probability of anything in a continuous function is 0 at a specific point.
z=(5.5-10)/sqrt (6)=-1.840
z=(4.5-10)/sqrt(6)=-2.24
Want z between -1.84 and -2.24
It is 0.0203
For >n use 5.5, we add 0.5 and go from there
Now it is z>-1.84, which is 0.9671.
For <=n, use 4.5, we subtract 0.5 and go from there.
That is z<-2.24 or probability of 0.0125.

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