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Introduction to Statistics: Sampling Distributions and Probability Calculations, Exams of Nursing

Chamberlain College of NursingNursing

A series of exercises and solved examples related to sampling distributions and probability calculations in statistics. it covers topics such as approximating sampling distributions with normal distributions, determining appropriate sample sizes for estimating population parameters, and calculating probabilities using z-scores. The examples provide step-by-step solutions, making it a valuable resource for students learning introductory statistics.

Typology: Exams

2024/2025

Available from 05/08/2025

Bihah-John
Bihah-John 🇺🇸

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Module 5-MATH 110 - Introduction to Statistics
Exam
Exam Page 1
Suppose that you take a sample of size 50 from a population that is not normally distributed. Can the
sampling distribu
ti
on of
x
be approximated by a normal probability distribu
ti
on?
Yes, the sample size can be approximated by a normal probablity ditribution because the sample size is
greater than 30.
Answer Key
Suppose that you take a sample of size 50 from a population that is not normally distributed.
Can the sampling distribu
ti
on of
x
be approximated by a normal probability distribu
ti
on?
Yes. The sample size is greater than 30, therefore, we may approximate by a normal
probability distribution.
pf3
pf4
pf5

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Module 5-MATH 110 - Introduction to Statistics

Exam Exam Page 1 Suppose that you take a sample of size 50 from a population that is not normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? Yes, the sample size can be approximated by a normal probablity ditribution because the sample size is greater than 30.

Answer Key

Suppose that you take a sample of size 50 from a population that is not normally distributed.

Can the sampling distribu ti on of x̄ be approximated by a normal probability distribu ti on?

Yes. The sample size is greater than 30, therefore, we may approximate by a normal

probability distribution.

Exam page 3

Suppose that you are attempting to estimate the annual income of 1200 families. In order to

use the infinite standard deviation formula, what sample size, n, should you use?

(n / N ) ≤0.

N = 1200

n ≤ (0.05 x 1200 ) = 60

n ≤ 60 The sample size (n) has to be less than or equal to 60 n ≤ 60 The sample size (n) has to be less than or equal to 60

Answer Key

Suppose that you are attempting to estimate the annual income of 1200 families. In order to

use the infinite standard deviation formula, what sample size, n, should you use?

In order to use infinite standard deviation formula, we should have:

n≤0.05(1200)

n≤

So, the sample size should be less than 60.

Exam Page 4 Suppose that in a very large city 9.8 % of the people have more than two jobs. Suppose that you take a random sample of 70 people in that city, what is the probability that 9 % or more of the 70 have more than two jobs? We want P(Z>-0.23). From the standard normal table, we find: P(Z>-.23)=1- P(Z<-.23)=1-.40905=.59095. So there is a .60257 probability that the percentage of the sample that have more than two jobs is more than 9 %.

-1.0 points Instructor Comments The value stated in the conclusion is not correct.

Answer Key

Suppose that in a very large city 9.8 % of the people have more than two jobs.

Suppose that you take a random sample of 70 people in that city, what is the

probability that 9 % or more of the 70 have more than two jobs?

Now we find the z-score:

We want P(Z>-0.23). From the standard normal table, we find:

P(Z>-.23)=1- P(Z<-.23)=1-.40905=.59095.

So there is a .60257 probability that the percentage of the sample that have

more than two jobs is more than 9 %.