Question

The normal approximation of the binomial distribution is appropriate when

*np* ≥ 5.

*n*(1 − *p*) ≥ 5.

*np* ≤ 5.

*n*(1 −
*p*) ≤ 5 and *np* ≤ 5.

*np* ≥ 5 and *n*(1 − *p*) ≥ 5.

Answer #1

np ≥ 5 and n(1 − p) ≥ 5.

By using some mathematics it can be shown that there are a few
conditions that we need to use a normal approximation to the
binomial distribution. The number of observations *n* must
be large enough, and the value of *p* so that both
*np* and *n*(1 - *p*) are greater than or
equal to 5. This is a rule of thumb, which is guided by statistical
practice. The normal approximation can always be used, but if these
conditions are not met then the approximation may not be that good
of an approximation.

The normal approximation of the binomial distribution is
appropriate when:
A. np 10
B. n(1–p) 10
C. np ≤ 10
D. np(1–p) ≤ 10
E. np 10 and n(1–p) 10

If np≥5 and nq≥5, estimate P(fewer than 6) 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.

1. Normal Approximation to Binomial Assume
n = 10, p = 0.1.
a. Use the Binomial Probability function to compute the P(X =
2)
b. Use the Normal Probability distribution to approximate the
P(X = 2)
c. Are the answers the same? If not, why?

Suppose that x has a binomial distribution with n
= 202 and p = 0.47. (Round np and n(1-p) answers
to 2 decimal places. Round your answers to 4 decimal places. Round
z values to 2 decimal places. Round the intermediate value (σ) to 4
decimal places.)
(a) Show that the normal approximation to the
binomial can appropriately be used to calculate probabilities about
x
np
n(1 – p)
Both np and n(1 – p) (Click to select)≥≤
5
(b)...

A binomial distribution has p? = 0.26 and n? = 76. Use the
normal approximation to the binomial distribution to answer parts
?(a) through ?(d) below.
?a) What are the mean and standard deviation for this?
distribution?
?b) What is the probability of exactly 15 ?successes?
?c) What is the probability of 14 to 23 ?successes?
?d) What is the probability of 11 to 18 ?successes

Normal Approximation to Binomial
Assume n = 100, p = 0.4.
Use the Binomial Probability function to compute the P(X =
40)
Use the Normal Probability distribution to approximate the P(X
= 40)
Are the answers the same? If not, why?

Suppose X is binomial random variable with n = 18 and p = 0.5.
Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to
find the exact probabilities and their normal approximations. In
case you don’t remember the formula, for a binomial random variable
X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X
= 14). (b) P(X ≥ 1).

np, nq formula
A) Explain when you can use normal distribution to approximate
the binomial distribution
B) If we already know the binomial probability distribution
formula, why do we need to know this one?
C)When is it useful to approximate the binomial distribution as
normal. Provide 1 example

If it is appropriate to do so, use the normal approximation to
the p^ p^ -distribution to calculate the
indicated probability:
Standard Normal Distribution Table
n=80,p=0.715n=80,p=0.715
P( p̂ > 0.75)P( p̂ > 0.75) =
Enter 0 if it is not appropriate to do so.
Please provide correct answer. thanks

If np greater than or equals 5 and nq greater than or equals 5,
estimate Upper P left parenthesis fewer than 5 right parenthesis
with n=13 and p=0.4 by using the normal distribution as an
approximation to the binomial distribution; if np less than 5 or
nq less than5, then state that the normal approximation is not
suitable.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 4 minutes ago

asked 8 minutes ago

asked 10 minutes ago

asked 18 minutes ago

asked 26 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 33 minutes ago

asked 33 minutes ago

asked 33 minutes ago

asked 35 minutes ago