Question

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))

Answer #1

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>3) P ( X > 3 ) , n=7 n = 7 , p=0.5 p = 0.5

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

Assume the random variable X has a binomial distribution with
the given probability of obtaining success. Find the following
probability, given the number of trials and the probability of
obtaining success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.3

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.5

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X<5) n=8, p=0.4

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X < 4) , n = 8, p = 0.3

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).

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>3)P(X>3), n=5, p=0.8

If the random variable X follows a binomial distribution with
the probability of success given
by p, show that the variance of X is equal to np(1-p).
[Hint:Consider first a Bernoulli probability distribution with
n=1.]

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≤4), n=6, p=0.8

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