Question

Compute the probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes.

The probability of 6 success is?

Answer #1

Binomial Probability Distribution: For a random variable X, given the probability of success is p, and probability of failure is q = (1-p), the probability of obtaining x successes in n independent trials of a binomial experiment, is

The probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes is

Here,

Sample size n=11,

No. of successes r = 6,

Probability of success p = (No of successes)/ Population size = 25/70 = 0.36

Probability of failure q = 1-p = 1- 0.36 = 0.64

Thus, probability of 6 successes is

= 0.1079 = 0.11

The probability of 6 successes in a random sample of size n=11 obtained from a population of size N=70 that contains 25 successes is 0.11.

A simple random sample size of n=800 is obtained from a
population whose size is N=10,000,000 and whose population
proportion with a specified characteristic is p=.32.
a)describe the sampling distribution
b) What is the probability of obtaining x=350 or more
individuals with the characteristic?

A simple random sample size of n = 75 is obtained from a
population whose size is N = 10000 and whose population proportion
with a specified characteristic is p = 0.8.
a) What is the probability of obtaining x = 63 or more
individuals with the characteristic?
b) Construct a 90% interval for the population proportion if x =
30 and n = 150.

A random sample of size n=55 is obtained from a
population with a standard deviation of σ=17.2, and the
sample mean is computed to be x=78.5.
Compute the 95% confidence interval.
Compute the 90% confidence interval.
SHOW WORK

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...

A simple random sample of size n=11 is obtained from a
population with μ=68 and σ=17.
(a) What must be true regarding the distribution of the
population in order to use the normal model to compute
probabilities involving the sample mean? Assuming that this
condition is true, describe the sampling distribution of barx.
(b) Assuming the normal model can be used, determine P(bar x
< 71.4).
(c) Assuming the normal model can be used, determine P(bar x
≥ 69.6).

A random sample of n = 25 is obtained from a population with
variance 2 , and the sample mean is computed to
be = 70. Consider the null hypothesis H0 : =
80 against H1 : < 80 and compute the p-value when
2 = 600.

8. A random sample of size n = 75 is obtained from a population
whose size is N = 12,000 and whose population proportion with a
specified characteristic is P =0.8 . Describe the sampling
distribution of p.

Suppose a simple random sample of size n=75 is obtained from a
population whose size is N= 25,000
and whose population proportion with a specified characteristic
is p=0.2.
(c) What is the probability of obtaining x=99
or fewer individuals with the characteristic? That is, what
is
P(p ≤ 0.12)?
(Round to four decimal places as needed.)

Suppose a simple random sample of size n=150 is obtained from a
population whose size is N=30,000 and whose population proportion
with a specified characteristic is p= 0.2
What is the probability of obtaining x=36 or more individuals
with the characteristic? That is, what is P(p≥0.24)?
P( p≥0.24)=________
(Round to four decimal places as needed.)

Suppose a simple random sample of size n=1000 is obtained from a
population whose size is N=1,500,000 and whose population
proportion with a specified characteristic is p=0.55 .
a) What is the probability of obtaining x=580 or more
individuals with the characteristic?
P(x ≥ 580) = (Round to four decimal places as
needed.)
(b) What is the probability of obtaining x=530 or fewer
individuals with the characteristic?
P(x ≤ 530) = (Round to four decimal places as
needed.)

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