SOLUTION: If np ≥ 5 and nq ≥ ​5, estimate P(at least 5) with n = 13 and p = 0.5 by using the normal distribution as an approximation to the binomial​ distribution; if np < 5 or nq <

Algebra ->  Probability-and-statistics -> SOLUTION: If np ≥ 5 and nq ≥ ​5, estimate P(at least 5) with n = 13 and p = 0.5 by using the normal distribution as an approximation to the binomial​ distribution; if np < 5 or nq <       Log On


   

Question 1182747: If np ≥ 5 and nq ≥ ​5, estimate P(at least 5) with n = 13 and p = 0.5 by using the normal distribution as an approximation to the binomial​ distribution; if np < 5 or nq < ​5, then state that the normal approximation is not suitable.
Select the correct choice below​ and, if​ necessary, fill in the blank to complete your choice.
A. P(at least 5) = __
(Round to three decimal places as​ needed.)
B. The normal distribution cannot be used.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
n = 13, p = 0.5, q = 1-0.5 = 0.5
np = (13)(0.5) = 6.5 ≥ 5
nq = (13)(0.5) = 6.5 ≥ 5

mu=np=6.5
sigma=sqrt%28n%2Ap%2Aq%29=sqrt%2813%2A0.5%2A0.5%29=1.802775638

Since it's ≥ and not > and to the right, we use 5-0.5 = 4.5
because going right from 4.5 includes 5.  

P(x > 4.5) with μ = 6.5 and σ = 1.802775638

Either find z-score and use table or use technology to find

Answer = 0.866

Edwin