(a) With n equals=1313 and p equals=0.50.5, find Upper P left parenthesis at lea

Question

(a) With n equals=1313
and
p equals=0.50.5,
find
Upper P left parenthesis at least 4 right parenthesisP(at least 4)
using a binomial probability table.

(b) If
np greater than or equals 5np5
and nq greater than or equals 5nq5, also estimate
Upper P left parenthesis at least 4 right parenthesisP(at least 4)
by using the normal distribution as an approximation to the binomial distribution; if
np less than<5 or nq less than<5,then state that the normal approximation is not suitable.

(a) Find the probability by using a binomial probability table.
Upper P left parenthesis at least 4 right parenthesisP(at least 4)equals=0.9540.954
(Round to three decimal places as needed.)
(b) Estimate the probability using the normal distribution. If the normal distribution cannot be used to approximate this probability, then enter 'N'.
Upper P left parenthesis at least 4 right parenthesis

P(at least 4)equals=
(Round to three decimal places as needed.)

Explanation / Answer

a. This is binomial with n=13 and p=0.5

P(x)=ncxp^x(1-p)^n-x

P(x>=4)=0.9539

b. Here np=6.5 and nq=6.5>=5

So we will use approximation of normal

sd=sqrt(npq)=1.80

So P(x>=4)=P(z>=4-6.5/1.80)=P(z>=-1.389)=0.5-P(0<=z<=-1.389)=0.5+4176=0.9176

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