Question

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

Answer #1

Using your knowledge of Binomial Distribution find:
a. P(5) if p = 0.3, n = 7 Answer with at least 5 decinal
places.
b. P(x < 3) if p = 0.65, n = 5
c. P(x > 4) if p = 0.25, n = 6
d. P(at least one) if p = 0.45, n = 6
e. (A-Grade) P(x ≤ 17) if p = 0.75, n = 20

Suppose that Y has a binomial distribution with
p = 0.60.
(a)
Use technology and the normal approximation to the binomial
distribution to compute the exact and approximate values of
P(Y ≤ μ + 1)
for n = 5, 10, 15, and 20. For each sample size, pay
attention to the shapes of the binomial histograms and to how close
the approximations are to the exact binomial probabilities. (Round
your answers to five decimal places.)
n = 5
exact value...

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).

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)...

Let X ∼ Binomial(20, 0.3).
(a) Find the exact P(10 < X ≤ 16) in numerical form.
(b) Propose a Normal distribution W that match well with X.
(c) Approximate the probability in (a) using the Normal
distribution in (b), 0.5 correction factor should be taken into
consideration.

approximate the following binomial probabilities for
this continuous probability distribution
p(x=18,n=50,p=0.3)
p(x>15,n=50,p=0.3)
p(x>12,n=50,p=0.3)
p(12<x<18,n=50,p,=0.3)

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=62, p=0.3 and X=16
A. find P(X)
B. find P(x) using normal distribution
C. compare result with exact probability

Let X denote a random variable that follows a binomial
distribution with parameters n=5, p=0.3, and Y denote a random
variable that has a Poisson distribution with parameter λ = 6.
Additionally, assume that X and Y are independent random
variables.
Using the joint pdf function of X and Y, set up the summation
/integration (whichever is relevant) that gives the expected value
for X, and COMPUTE its value.

Let X denote a random variable that follows a binomial
distribution with parameters n=5, p=0.3, and Y denote a random
variable that has a Poisson distribution with parameter λ = 6.
Additionally, assume that X and Y are independent random
variables.
Using the joint pdf function of X and Y, set up the summation
/integration (whichever is relevant) that gives the expected value
for X, and COMPUTE its value.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago