SOLUTION: 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 norma

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

RELATED QUESTIONS
If np greater than or equals 5np≥5 and nq greater than or equals... (answered by ikleyn)

If np greater than or equals ≥5 and nq greater than or equals ≥5, estimate... (answered by ikleyn)

If np is greater than or equal to 5 and nq is greater than or equal to 5 estimate P (more (answered by stanbon)

If np>=5 and nq>=5, estimate Upper P left parenthesis more than 7 right parenthesis with... (answered by stanbon)

If np is greater than or equal to nq is greater than or equal to, estimate P (more than... (answered by ewatrrr)

If np ≥ 5 and nq ≥ 5, estimate P(fewer than 5) with n = 14 and p = 0.6 by... (answered by rothauserc)

In np > 5 & nq > 5, estimate p (fewer than 7) with n=14 & p=0.6 by using the normal... (answered by ewatrrr)

If np ≥ 5 and nq ≥ 5, estimate P(fewer than 7) with n = 14 and p = 0.5 by using... (answered by Boreal)

Upper P left parenthesis x overbar greater than 89.65 right... (answered by ikleyn)