Np>5 and nq>5, estimate P(at least 11) with n=13 and p = 0.6 by using the normal distributions as an approximation to the binomial distribution. if np<5 or nq<5 then state the normal approximation is not suitable.p (at least 11) = ?

DofotheroU 2021-01-27 Answered

Np>5 and nq>5, estimate P(at least 11) with n=13 and p = 0.6 by using the normal distributions as an approximation to the binomial distribution. if np<5ornq<5 then state the normal approximation is not suitable.
p (at least 11) = ?

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hesgidiauE
Answered 2021-01-28 Author has 106 answers

Step 1
Given n=12 and p=0.6.
Then,
Mean = np
=13×0.6
=7.8
Standard deviation =np(1p)
=7.8(10.6)
=3.12
=1.7663
Step 2
So,
P(X11)=P(Xmeanstandarddeviation11meanstandarddeviation)
=P(Z117.81.7663)
=P(Z1.81) From the right tailed z - table.
=0.4649
Therefore, p (at least 11)=0.4649

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