Question

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

- M
**ake 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)

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 = 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)...

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.

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.

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

A drug test is accurate 95% of the time. If the test is given to
200 people who have not taken drugs, what is the probability that
exactly 191 will test negative?
First, use the normal approximation to the binomial, and use the
continuity correction.
Normal Approximate Probability = ?
Now use the binomial distribution.
Exact Binomial Probability = ?
Does the normal distribution make a pretty good approximation to
the binomial, in this case?
No, those probabilities are far...

Let
X be a binomial random variable with parameters n = 500 and p =
0.12. Use normal approximation to the binomial distribution to
compute the probability P (50 < X ≤ 65).

Compute P(x) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(x) using the normal
distribution and compare the result with the exact probability.
n=73 p=0.82 x=53
a) Find P(x) using the binomial probability distribution:
P(x) =
b) Approximate P(x) using the normal distribution:
P(x) =
c) Compare the normal approximation with the exact
probability.
The exact probability is less than the approximated probability
by _______?

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
n=50, p=0.50, and x=17 For n=50, p=0.5, and X=17, use the
binomial probability formula to find P(X).
Q: By how much do the exact and approximated probabilities
differ?
A. ____(Round to four decimal places as needed.)
B. The normal distribution cannot be used.

Suppose X follows the Binomial Distribution with n=1000 and
p=0.002. Use the Poisson approximation to determine the probability
that X is at least 2.

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