Question

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).

Answer #1

Let X be a binomial random variable with n =
100 and p = 0.2. Find approximations to these
probabilities. (Round your answers to four decimal places.)
(c) P(18 < X < 30)
(d) P(X ≤ 30)

Suppose that a random variable X has a binomial distribution
with n=2, p=0.5. Find the mean and variance of Y =
X2

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)...

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)

if X is a binomial random variable with n = 20, and p = 0.5,
then Select one: a. P(X = 20) = P(19 ≤ X ≤ 21) b. P(X = 20) = 1.0
c. P(X = 20) = 1 – P(X ≤ 20) d. P(X = 20) = 1 – P(X ≥ 0) e. None of
the suggested answers are correct

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.

x is a binomial random variable with n=10 and p=.5. find the
probability of obtaining from 6 to 9 tails of a fair coin. use the
binomial probability distribution formula

Assume that X is a binomial random variable with
n = 15 and p = 0.78. Calculate the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
Assume that X is a binomial random variable with
n = 15 and p = 0.78. Calculate the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
a.
P(X = 14)
b.
P(X = 13)
c.
P(X ≥ 13)

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
np ≥ 5.
n(1 − p) ≥ 5.
np ≤ 5.
n(1 −
p) ≤ 5 and np ≤ 5.
np ≥ 5 and n(1 − p) ≥ 5.

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