Question

#1.If

npgreater than or equals≥5

and

nqgreater than or equals≥​5,

estimate

Upper P left parenthesis more than 5 right parenthesisP(more than 5)

with

nequals=1212

and

pequals=0.30.3

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.

2. If

npgreater than or equals≥5

and

nqgreater than or equals≥​5,

estimate

Upper P left parenthesis at least 10 right parenthesisP(at least 10)

with

nequals=1313

and

pequals=0.60.6

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.

Answer 1

1. If np≥5 and nq≥​5, estimate P(more than 5) with n=12 and p=0.3 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.

The normal approximation is not suitable.

2. If np≥5 and nq≥​5, estimate P(at least 10) with n=13 and p=0.6 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.

µ = n*p = 13*0.6 = 7.8

σ = √n*p*(1 - p) = √13*0.6*(1 - 0.6) = 1.766

P(at least 10) = (10 - 7.8)/1.766 = 1.25

The probability is 0.1065.