Question

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

Answer #1

**Answer to the
question:**

** Option E:** np = 10 and n(1–p) = 10.

** Explanation:** The binomial distribution
is approximate by normal distribution if both np and n(1-p) is
atleast greater or equal to zero. Here, where p is the probability
of success and the (1-p)=q is the probability of failure. Since,
both np=nq=10>5, this is the normal approximation of the
binomial distribution.

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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.

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?

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

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.

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)...

Suppose that x has a binomial distribution with n = 199 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)...

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

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).

We provided the rule of thumb that the normal approximation to
the binomial distribution is adequate if p ± 3
pq
n
lies in the interval (0, 1)—that is, if 0 < p − 3
pq
n
and p + 3
pq
n
< 1,
or, equivalently,
n > 9 (larger of p and q/smaller of p and q)
(a) For what values of n will the normal approximation
to the binomial distribution be adequate if p = 0.5?.
(b) Answer...

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