Question

If

np greater than or equals 5np≥5

and

nq greater than or equals 5nq≥5​,

estimate

Upper P left parenthesis fewer than 4 right parenthesisP(fewer than 4)

with

nequals=1414

and

pequals=0.40.4

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 4 right parenthesisP(fewer than 4)equals=

nothing

​(Round to four decimal places as​ needed.)

B.

The normal approximation is

Answer 1

Solution

n = 14

p = 0.4

q = 1-p = 0.6

np = 0.4*14 = 5.6 >= 5

nq = 0.6*14 = 8.4 >= 5

hence we have to use normal approximation

Mean = np = 5.6

Standard Deviation = sqrt(npq) = 2.3664

P(fewer than 4) = p(x<4) = p(x < 3.5) = p(z<(3.5-mean)/standard deviation)

= p(z<-0.88)

= 0.1894

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