Question

Determine which of the following binomial distributions has approximately normal distribution

n = 40, p = 0.02

or

n = 400, p = 0.002

or

none

Answer #1

Determine which of the following binomial distributions has
approximately normal distribution

For which of the following binormial distributions are the
conditions for the normal approximation to the binomial
distribution satisfied?
a. = 40, p = 0.9
b. = 400, p = 0.99
c. = 20, p = 0.2
d. = 20, p = 0.3

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.

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

Let X be a binomial random variable with n =
400 trials and probability of success p = 0.01. Then the
probability distribution of X can be approximated by
Select one:
a. a Hypergeometric distribution with N =
8000, n = 400, M = 4.
b. a Poisson distribution with mean 4.
c. an exponential distribution with mean 4.
d. another binomial distribution with n =
800, p = 0.02
e.
a normal distribution with men 40 and variance 3.96.

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 has a binomial distribution with p = 0.3 and n = 20.
Note that E[X] = 6. Compute P(5 <X < 8) exactly and
approximately with the CLT. Answers: 0.4851 from normal, 0.4703
from exact computation.
please write the process

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)

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.

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 _______?

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