Question

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).

Answer #1

Solution:

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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.
Derive the joint probability distribution function for X and Y.
Make sure to explain your steps.

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.

Let
x be binomial random variable with n=50 and p=.3. The probability
of less than or equal to 13 successes, when using the normal
approximation for binomial is ________. (Please show how to work
the problem).
a) -.6172
b) .3086
c) 3.240
d) .2324
e) .2676
f) -.23224

X is a binomial random variable with n = 15 and p = 0.4.
a. Find using the binomial distribution.
b. Find using the normal approximation to the binomial
distribution.

The random variable X has a Binomial distribution with
parameters n = 9 and p = 0.7
Find these probabilities: (see Excel worksheet)
Round your answers to the nearest hundredth
P(X < 5)
P(X = 5)
P(X > 5)

Assume that x is a binomial random variable with n and p as
specified below. For which cases would it be appropriate to use
normal distribution to approximate binomial distribution? a. n=50,
p=0.01 b. n=200, p=0.8 c. n=10, p=0.4

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.

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

Let x be a binomial random variable with n = 25 and the
probability of failure is 0.4. Using the normal distribution to
approximate the binomial, determine the probability that more than
12 successes will occur.
A. 0.8461
B. 0.1539
C. 0.9192
D. 0.0329

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