Find the normal approximation for the binomial probability P(x = 4, 5), where n

Question

Find the normal approximation for the binomial probability P(x = 4, 5), where n = 14 and p = 0.5. Compare this to the value of P(x = 4, 5) obtained from Table 2 in Appendix B. Find the normal approximation for the binomial probability P(x lessthanorequalto 8), where n = 14 and p = 0.4. Compare this to the value of P(x lessthanorequalto 8) obtained from Table 2 in Appendix B. Find the normal approximation for the binomial probability P(x greaterthanorequalto 9), where n = 13 and p = 0.7. Compare this to the value of P(x greaterthanorequalto 29) obtained from Table 2 in Appendix B.

Explanation / Answer

6.39)mean =np=14*0.5=7

std deviation=(np(1-P))1/2 =1.87

from normal distribution:

P(4<=X<=5)=P((3.5<X<5.5)=P(-1.8708<Z<-0.8018)=0.2113-0.0307=0.1807

from binomial distribution P(4<=X<=5)=0.1833

6.40)mean =5.6

std deviation 1.4967

P(X<=8)=P(X<8.5)=P(Z<1.9376)=0.9737

from bionomial dist. P(X<=8)=0.9417

6.41) mean =9.1

std deviation =2.5239

P(X>=9)=1-P(X<8.5)=1-P(Z<-0.2377)=1-0.4060=0.5940

from binomial :P(X>=9)=0.6543

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