If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x=3) for n=10, p=0.5
b. P(x≤4) for n=15, p=0.3
c. P(x>1) for n=5, p=0.2
d. P(x<6) for n=15, p=0.8
e. P(x≥14) for n=25, p=0.8
f. P(x=3) for n=20, p=0.1
Probability Mass Functions, Random
Variables
Find a table of the Binomial random variable (include a picture
of the table in your submission) and obtain the probability that in
20 independent trials, each of which has probability of success
equal to 0.1, the number of successes is less than or equal to
3.
Repeat the problem using instead of a Binomial a Poisson with
suitable parameter lambda.
Let X represent a binomial random variable with n = 360 and p = 0.82. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.
Probability
a.
P(X ≤ 290)
b.
P(X > 300)
c.
P(295 ≤ X ≤ 305)
d.
P(X = 280)
0.0063
Use Excel to generate the probability distribution for a
binomial random variable for which there are 20 trials (n = 20) and
the probability of success is 0.5 (p = 0.5), and show the
graph.
Determine whether or not the random variable X is a binomial
random
variable.
(a)
X is the number of dots on the top face of a fair die
(b)
X is the number of hearts in a five card hand drawn (without
replacement) from a well
shuffled ordinary deck.
(c)
X is the number of defective parts in a sample of ten randomly
selected parts coming from a manufacturing process in which 0.02%
of all parts are defective.
(d)
X...
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=6), 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≤4), n=7, p=0.6
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=14), n=15, p=0.7
Make an example of a binomial experiment and its binomial random
variable X (Do not use a coin-flipping example, anything else is
fine)
What is your trial? How many trials (which is n) do you have?
Why do you think they are independent which is one of the required
conditions for the binomial experiments?
Which outcome of your trial is considered a success?
The probability of having a success per trial, P. Give the
probability value of P. If you...
Make an example of a binomial experiment and its binomial random
variable X (Do not use a coin-flipping example, anything else is
fine)
What is your trial? How many trials (which is n) do you have?
Why do you think they are independent which is one of the required
conditions for the binomial experiments?
Which outcome of your trial is considered a success?
The probability of having a success per trial, P. Give the
probability value of P. If you...