MATH 225N Week 5 Assignment / MATH225 Week 5 Assignment : Central Limit Theorem for Means(New-2021):Chamberlain College of Nursing (ANSWERS VERIFIED)

MATH225 Week 5 Assignment: Central Limit Theorem for Means

1. Question

A family of statisticians is trying to decide if they can afford for their child to play youth
baseball. The cost of joining a team is normally distributed with a mean of $750 and a

standard deviation of $185 . If a sample of 40 teams is selected at random from the
population, select the expected mean and standard deviation of the sampling
distribution below.

Correct answer:
σx¯=$29.25
μx¯=$750

The standard deviation of the sampling distribution

σx¯=σn−−√=$18540−−√=$29.25

When the distribution is normal the mean of the sampling distribution is equal to the
mean of the population μx¯=μ=$750 .


Question

A cupcake baker is planning a supplies order and needs to know how much flour he
needs. He knows that his recipes use an average of 100 grams of flour, normally
distributed, with a population standard deviation of 15 grams. If he is consulting a

sample size of 30 recipes, select the mean and standard deviation of the sampling
distribution to help him order his supplies from the options below.

σx¯=2.74 grams
μx¯=100 grams

The standard deviation of the sampling distribution is

σx¯=σn−−√=1530−−√=2.74 grams

, Likewise, when the distribution is normal the mean of the sampling distribution is equal
to the mean of the population μx¯=μ=100 grams.


Question

A head librarian for a large city is looking at the overdue fees per user system-wide to
determine if the library should extend its lending period. The average library user has

$19.67 in fees, with a standard deviation of $7.02 . The data is normally distributed and
a sample of 72 library users is selected at random from the population. Select the
expected mean and standard deviation of the sampling distribution from the options
below.

Correct answer:
σx¯=$0.83
μx¯=$19.67

The standard deviation of the sampling distribution is

σx¯=σn−−√=$7.0272−−√=$0.83

When the distribution is normal, the mean of the sampling distribution is equal to the

mean of the population μx¯=μ=$19.67 .




2. Question

A well known social media company is looking to expand their online presence by
creating another platform. They know that they current average 2,500,000 users each
day, with a standard deviation of 625,000 users. If they randomly sample 50 days to
analyze the use of their existing technology, identify each of the following, rounding to
the nearest whole number if necessary:

, We are given population mean μ=2,500,000 and population standard deviation
σ=625,000 , and want to find the mean and standard error of the sampling distribution,
μx¯ and σx¯ for samples of size n=50 .

By the Central Limit Theorem, the means of the two distributions are the same:

μx¯=μ=2,500,000

To find the Standard Deviation of the sampling distribution, we divide the population
standard deviation by the square root of the sample size:

σx¯=σn−−√=625,00050−−√≈88,388




3. Question

A bank is reviewing its risk management policies with regards to mortgages. To
minimize the risk of lending, the bank wants to compare the typical mortgage owed by
their clients against other homebuyers. The average mortgage owed by Americans is
$306,500 , with a standard deviation of $24,500 . Suppose a random sample of 150
Americans is selected.

Identify each of the following, rounding your answers to the nearest cent when
appropriate:

 1306500$306500$306500
 224500$24500$24500
 3150$150$150
 4306500$306500$306500
 $2000.42

We are given population mean μ=$306,500 and population standard deviation
σ=$24,500 , and want to find the mean and standard error of the sampling distribution,
μx¯ and σx¯ for samples of size n=150 .

By the Central Limit Theorem, the means of the two distributions are the same:

μx¯=μ=$306,500