Question

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) Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probability: 1. P (x = 81) 2. P (x ≤ 98) 3. P (x < 77) 4. P (x ≥ 105) 5. P (x > 101)

Answer #1

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 = 200 and p = .4.
1. Show that the normal approximation to the binomial can
appropriately be used to calculate probabilities for
Make continuity corrections for each of the
following, and then use the normal approximation to the binomial to
find each probability:
P(x = 80)
P(x ≤ 95)
P(x < 65)
P(x ≥ 100)
P(x > 100)

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.

Use the normal approximation to the binomial to find the
probability for n=12 p=0.5 and x≥8. Round z-value calculations to 2
decimal places and final answer to 4 decimal places

A binomial probability distribution has p = 0.20 and n =
100.
(d) What is the probability of 17 to 23 successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)
(e) What is the probability of 14 or fewer successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)

If x is a binomial random variable where n = 100 and p = 0.20,
find the probability that x is more than 18 using the normal
approximation to the binomial. Check the condition for continuity
correction.

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

Let X be a binomial random variable with n = 10 and p = 0.2.
Find the following values. (Round your answers to three decimal
places.) (a) P(X = 4) (b) P(X ≥ 4) (c) P(X > 4) (d) P(X ≤ 4) (e)
μ = np μ = 2.00 (correct) (f) σ = npq σ = 1.265 (correct)

If x is a binomial random variable where n = 100 and p = 0.20,
find the probability that x is more than 18 using the normal
approximation to the binomial. Check the condition for continuity
correction
need step and sloution

Suppose Y is a random variable that follows a binomial
distribution with n = 25 and π = 0.4. (a) Compute the exact
binomial probability P(8 < Y < 14) and the normal
approximation to this probability without using a continuity
correction. Comment on the accuracy of this approximation. (b)
Apply a continuity correction to the approximation in part (a).
Comment on whether this seemed to improve the approximation.

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