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Question

I'm bewildered on this!!

 

If np ≥ 5 and nq ≥ 5, estimate P(fewer than 6) with n = 14 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.

P(fewer than 6) = ?

Answer 1

Since np≥5 and nq≥5 the normal approximation to the binomial applies. you should also use the correction for continuity.

 

P(x<6)  = p(X<5.5)   z=(5.5-np)(√npq) = -1.5/1.87 = -.8  calculate this z value and use the normal table:

 

see https://www.wyzant.com/resources/files/392716/normal_dist_table

 

to get the probability=.5-.2881 = .2119.

 

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