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

If random variable X has a binomial distribution with n =8 and
P(success) = p =0.5, find the probability that X is at most 3.
(That is, find P(X ≤ 3))

For a binomial random variable X, if np and n(1-p) are both at
least 5 what can we do?

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)...

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)

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.

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

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

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