Question

**A random sample of size 9 is selected from a certain
population.**

(i) Calculate, by hand, the probability that exactly eight of the nine selected values lie above the population median. Show your working.

(ii) Calculate, by hand, the probability that at least eight of the nine selected values lie above the population median. Again, show your working.

Answer #1

Median is the middle value. Therefore, in the population, 50% data lies above median.

This is a binomial distribution problem where:

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(i) The probability that exactly eight of the nine selected values lie above the population median is:

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(ii) The probability that at least eight of the nine selected values lie above the population median is:

Suppose a random sample of size 55 is selected from a population
with σ = 9. Find the value of the standard error of the mean in
each of the following cases (use the finite population correction
factor if appropriate).
a. The population size is infinite (to 2
decimals).
b. The population size is N = 50,000
(to 2 decimals).
c. The population size is N = 5000 (to
2 decimals).
d. The population size is N = 500 (to...

4. A population of size 200 consists of two strata, I and II. A
simple random sample of size 40 is drawn without replacement from
the population. (1) Suppose that strata I and II are of sizes 85
and 115 respectively. Let T be the number of selected individuals
from stratum I. What is the probability distribution of T?
(2) For Question (1), find the expectation and variance of
T.
(3) Suppose that you did not know the size of...

A random sample of size 16 is selected from a normal population
with a mean of 173 and a standard deviation of 12. What is the
probability that the sample mean will exceed 175? Give answer to
two decimal places.

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What is the mean of the xbar sampling distribution? =40
What is the standard deviation of the xbar sampling distribution
(to 3 decimal places)? =0.625
For parts b & c round to 4 decimal places:
(b) What is the probability that xbar will be within 0.5 of the
population mean μ ?
(c) What is the probability...

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What are the mean and standard deviation of the sampling
distribution?
μx =
σx =
(b) What is the approximate probability that x will be
within 0.4 of the population mean μ? (Round your answer to
four decimal places.)
P =
(c) What is the approximate probability that x will differ
from μ by more than 0.8?...

1.
Suppose that a random sample of size 36 is to be selected from a
population with mean 49 and standard deviation 9. What is the
approximate probability that will be within 0.5 of the
population mean?
a.
0.5222
b.
0.0443
c.
0.2611
d.
0.4611
e.
0.7389
2.
Suppose that x is normally distributed with a mean of 60 and a
standard deviation of 9. What is P(x 68.73)?
a.
0.834
b.
0.166
c.
0.157
d.
0.334
e.
0.170

A random sample size of 100 is to be taken from a population
that has a proportion equal to 0.35. The sample proportion will be
used to estimate the population proportion.
Calculate the probability that the sample proportion will be
within ±0.05 of the population proportion.
Illustrate the situation graphically, show the calculations, and
explain your results in a sentence.

Q4. A simple random sample of size n=180 is obtained from a
population whose size=20,000 and whose population proportion with a
specified characteristic is p=0.45. Determine whether the sampling
distribution has an approximately normal distribution. Show your
work that supports your conclusions.
Q5. Using the values in Q4, calculate the probability of
obtaining x=72 or more individuals with a specified
characteristic.

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.)

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What is the mean of the xbar sampling distribution? 40 What
is the standard deviation of the xbar sampling distribution?
.625
(b) What is the approximate probability that xbar will be within
0.5 of the population mean μ ?
(c) What is the approximate probability that xbar will differ
from μ by more than 0.7?

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