Population Sample Data, Binomial & Normal Distributions

1. Why do we want to assume that our sample data represent a population
distribution?

2. What are the differences between the binomial and normal distributions?

Thank you.

Solution Preview

PLEASE SEE RESPONSE ATTACHED (ALSO PRESENTED BELOW), INCLUDING ONE SUPPORTING ARTICLE. I HOPE THIS HELPS AND TAKE CARE.

RESPONSE:

1. Why do we want to assume that our sample data represent a population distribution?

We want to assume our sample represents a population distribution because we want to generalize our findings to the population. For example, if we researched a sample (N=30) of organizations and found that the team approach to management is more effective than authoritarian management style, we would want to conclude that this is true for all organizations (i.e., population). In order to do this, we must assume that our sample (N=30) is representative of the population of all organizations.

2. What are the differences between the binomial and normal distributions?

The main differences between the two distributions are in their location and scale parameters (mean and standard deviations) and in the overall shape of the distribution (bell-shaped versus not bell-shaped). Let's take a closer look at the two distributions.

a. Normal distributions are symmetrical and have a bell-shaped distribution.

The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. It is a ...

Solution Summary

This solution discusses normal distribution and why we want to assume that our sample data represent a population distribution. The differences between the binomial and normal distributions are also discussed. Many examples are provided as well as one supporting article for further reading.

Describe the properties of a normal distribution. Explain why there are an infinite number of normaldistributions. Why do you want to assume that your sample data represent a population distribution?

View the "Sampling Distribution of the Mean" within a Multimedia Presentation.
InteliBoard Assessment
1. The mean of the sampling distribution is equal to
a. the population standard deviation
b. the sample mean
c. the sample standard deviation
d. the population mean
e. none of the above
2. The standard error of t

Please see the attached file for the fully formatted problems.
1. Explain the difference between a discrete and a continuous random variable. Give two examples of each type of random variable.
2. Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
a

Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95.
Can Nathan use the normal curve area to approximate a binomial probability?

1. True or False? Replacement is allowed in binomial experiments. Explain your answer.
2. True or False? Two normaldistributions that have the same standard deviation have the same shape, regardless of the relationship between their means. Explain your answer.

It is estimated that the probability that the general population will live past their 85th birthday is 5.4%. Use the standard normal distribution to approximate this Binomial problem and answer the following questions.
Out of a sample of 600, what is the probability that fewer than 30 will live beyond their 85th birthday?

Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomial probability?

See the attached file.
Assume that women's height are normally distributed with a mean given by =63.4 in, and a standard deviation given by =2.7in.
If 1 woman is randomly selected, find the probability that her height is less than 64 in.
If 46 women are randomly selected find the probability that they have a mean height les

Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5.
Find the probability that x = 2 using the binomial tables.
Use the normal approximation to find the probability that x = 2