Question 1064324: If np greater than or equals 5 and nq greater than or equals 5, estimate Upper P left parenthesis fewer than 2 right parenthesis with nequals
13 and pequals 0.4 by using the normal distribution as an approximation to the binomial distribution; if npless than 5 or nqless than 5, then state that the normal approximation is not suitable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.Upper P left parenthesis fewer than 2 right parenthesis
equals (Round to four decimal places as needed.)
B.The normal approximation is not suitable.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Binomial distribution with n=13 and p=0.4. Want probability p <2. I think this is what you want. The normal approximation is met given the values stated.
np=5.2; n(1-p)=7.8
variance is np(1-p)=13*0.4*0.6=3.12
sqrt (variance)=sd=1.767
want p (value is less than 2, when mean is 5.2 and sd is 1.767)
z=(0-5.2)/1.767=-2.943
z=(2-5.2)/1.767=-1.811
probability is -2.943 < z < -1.811=0.0334
Compare with using binomial distribution
13C1(0.4)^1(0.6)^12=0.0113
13C0(0.6^13)=0.0113
Total is 0.0226
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