Question

If np greater than or equals 5(np≥5) and nq greater than or equals 5(nq≥5), estimate P(fewer than 4) with nequals=13 and p equals=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.

Answer #1

np = 13 * 0.5 = 6.5 >= 5

nq = 13 * 0.5 = 6.5 >= 5

Using Normal Approximation to Binomial

Mean = n * P = ( 13 * 0.5 ) = 6.5

Variance = n * P * Q = ( 13 * 0.5 * 0.5 ) = 3.25

Standard deviation = √(variance) = √(3.25) = 1.8028

P(X < x) = P(Z < (x - mean ) / SD )

P ( X < 4 ) = ?

Using continuity correction

P ( X < n - 0.5 ) = P ( X < 4 - 0.5 ) = P ( X < 3.5 )

Standardizing the value

Z = ( X - µ ) / σ

Z = ( 3.5 - 6.5 ) / 1.8028

Z = -1.66

P ( ( X - µ ) / σ ) < ( 3.5 - 6.5 ) / 1.8028 )

P ( X < 3.5 ) = P ( Z < -1.66 )

P ( X < 3.5 ) = **0.0485**

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Select the correct choice below and, if necessary, fill in the
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If
np greater than or equals 5np≥5
and
nq greater than or equals 5nq≥5,
estimate
Upper P left parenthesis fewer than 5 right parenthesisP(fewer
than 5)
with
nequals=14
and
pequals=0.4
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.

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...

If np greater than or equals 5 and nq greater than or equals 5,
estimate Upper P (more than 9 ) with n = 13 and p = 0.3 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.
Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
A. P(more than...

If np greater than or equals 5 and nq greater than or equals 5,
estimate Upper P left parenthesis fewer than 6 right parenthesis
with nequals14 and pequals0.5 by using the normal distribution as
an approximation to the binomial distribution; if npless than5 or
nqless than5, 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 6...

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estimate Upper P left parenthesis fewer than 5 right parenthesis
with nequals13 and pequals0.6 by using the normal distribution as
an approximation to the binomial? distribution; if npless than5 or
nqless than?5, then state that the normal approximation is not
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