Question

Given a random sample size n=1600 from a binomial probability distribution with P=0.40 do the following... with probability of 0.20 Find the number of successes is less than how many? Please show your work

Answer #1

We are given the distribution here as:

As the sample size here is very very large, the distribution could be approximated to a normal distribution here as:

From standard normal tables, we have here:

P(Z < -0.842) = 0.2

Therefore the number of successes is computed here as:

= Mean -0.842*Std Dev

**Therefore 623 is the required number of successes
here.**

Given a random sample of size of
n equals =3,600
from a binomial probability distribution with
P equals=0.50,
complete parts (a) through (e) below.
Click the icon to view the standard normal table of the
cumulative distribution function
.a. Find the probability that the number of successes is greater
than 1,870.
P(X greater than>1 comma 1,870)
(Round to four decimal places as needed.)b. Find the
probability that the number of successes is fewer than
1 comma 1,765.
P(X less than<1...

A random sample of size n = 50 is selected from a
binomial distribution with population proportion
p = 0.8.
Describe the approximate shape of the sampling distribution of
p̂.
Calculate the mean and standard deviation (or standard error) of
the sampling distribution of p̂. (Round your standard
deviation to four decimal places.)
mean =
standard deviation =
Find the probability that the sample proportion p̂ is
less than 0.9. (Round your answer to four decimal places.)

Let
x be binomial random variable with n=50 and p=.3. The probability
of less than or equal to 13 successes, when using the normal
approximation for binomial is ________. (Please show how to work
the problem).
a) -.6172
b) .3086
c) 3.240
d) .2324
e) .2676
f) -.23224

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 = 6, p = 0.3
How do I determine if the answer should be Probability result or
Cumulative result?
Can you show me how to create a formula in excel to solve this
problem?...

Consider a binomial probability distribution with p=.35 and n=7.
what is the probability of the following?
a. exactly three successes P(x=3)
b. less than three successes P(x<3)
c. five or more successes P(x>=5)

Given a binomial random variable with n = 48 and p = 0.62 find
the probability of obtaining more than 21 but no
more than 34 successes to three decimal places.

Develop an algorithm for generation a random sample of size
N from a binomial random variable X with the
parameter n, p.
[Hint: X can
be represented as the number of successes in n independent
Bernoulli trials. Each success having probability p, and
X =
Si=1nXi
, where Pr(Xi = 1) = p, and
Pr(Xi = 0) = 1 – p.]
(a) Generate a sample of size
32 from X ~ Binomial (n = 7, p = 0.2)
(b) Compute...

Assuming the binomial distribution applies with a sample size of
nequals10, find the values below. a. the probability of 5 or more
successes if the probability of a success is 0.65 b. the
probability of fewer than 4 successes if the probability of a
success is 0.20 c. the expected value of the random variable if the
probability of success is 0.55 d. the standard deviation of the
random variable if the probability of success is 0.55

Suppose we have a binomial distribution with n trials
and probability of success p. The random variable
r is the number of successes in the n trials, and
the random variable representing the proportion of successes is
p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four...

A binomial probability distribution has p = 0.20 and n =
100.
(d) What is the probability of 17 to 23 successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)
(e) What is the probability of 14 or fewer successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)

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