Calculate each binomial
probability:
(a)
Fewer than 4 successes in 9 trials with a 10 percent chance of
success. (Round your answer to 4 decimal
places.)
Probability
(b)
At least 1 successe in 5 trials with a 10 percent chance of
success. (Round your answer to 4 decimal
places.)
Probability
(c)
At most 11 successes in 19 trials with a 70 percent chance of
success. (Round your answer to 4 decimal
places.)
...
Let the probability of success on a Bernoulli trial be 0.20. a.
In nine Bernoulli trials, what is the probability that there will
be 8 failures? (Round your final answers to 4 decimal places.)
Probability b. In nine Bernoulli trials, what is the probability
that there will be more than the expected number of failures?
(Round your final answers to 4 decimal places.) Probability
Suppose 4 Bernoulli trials, each with success probability p, are
conducted such that the outcomes of the 4 experiments are mutually
independent. Let the random variable X be the total number of
successes over the 4 Bernoulli trials.
(a) Write down the sample space for the experiment consisting of
4 Bernoulli trials (the sample space is all possible sequences of
length 4 of successes and failures you may use the symbols S and
F).
(b) Give the support (range) X...
Shown below are the number of trials and success probability for
some Bernoulli trials. Let X denote the total number of
successes.
n = 6 and p = 0.3
Determine P(x=4) using the binomial probability formula.
b. Determine P(X=4) using a table of binomial
probabilities.
Compare this answer to part (a).
Calculate each binomial probability:
(a) Fewer than 5 successes in 11 trials with a 10
percent chance of success. (Round your answer to 4 decimal
places.)
Probability =
(b) At least 2 successes in 8 trials with a 30
percent chance of success. (Round your answer to 4 decimal
places.)
Probability =
(c) At most 10 successes in 18 trials with a 70
percent chance of success. (Round your answer to 4 decimal
places.)
Probability = ...
. In a sequence of 7 Bernoulli trials with probability of
success p, let X be the number of successes not followed
immediately by a failure. Find E(X) (you can use indicators)
Negative Binomial experiment is based on sequences of Bernoulli
trials with probability of success p. Let x+m be the number of
trials to achieve m successes, and then x has a negative binomial
distribution. In summary, negative binomial distribution has the
following properties
Each trial can result in just two possible outcomes. One is
called a success and the other is called a failure.
The trials are independent
The probability of success, denoted by p, is the same on every...
Determine whether a probability model based on Bernoulli
trials can be used to investigate the situation. If not,
explain.
A company realizes that 5% of its pens are defective. In a package
of 30 pens, is it likely that more than 6 are defective? Assume
that pens in a package are independent of each other.
Group of answer choices
Yes
No. There are more than two possible outcomes.
No. 6 is more than 10% of 30
No, the chance of...
We know that based on the Binomial distribution, probability of
x successes in n trials when the probability of success is (p) can
be calculated by multiplying Combinations of n items x by x,
multiplied by the probability of success (p) raised to (x) and
multiplied by (1-p) raised to (n-x).
1. If probability of having a child who will study business in
college (probability of success) is 0.25, what is the probability
of a family with 6 children will...