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Essay Instructions: Please answer the following questions with 300 :

1. Define a normal distribution. Show the step that you use to compute the probability by using a normal distribution with specific mean and specific variance (you can choose suitable values for the mean and variance in your example).
2. State the central limit theorem. Describe simple random sampling. How would the sample mean of a simple random sampling be distributed? Give a numerical example showing that you calculated the likely hood of a sample mean to exceed a given value when the population mean, variance and the sample size is known?
3. Describe the difference between and point estimate and an interval estimate. Give a numerical example showing the steps of constructing a confidence interval for a population mean.

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Essay Instructions: Suggest one psychological research question that could be answered by each of the following types of statistical tests:
z test
t test for independent samples, and
t test for dependent samples


Standard score??"Also known as a z-score. A standard score gives us the position of a data value comparison to the mean. We also knew, by looking at the z score, whether this was a great score or not. Remember that a z score tells you, in standard deviation units, how far away the score is from the mean. Positive scores are above the mean while negative scores are below the mean. A z-score of 2.12 on a national exam is great. We have scored 2.12 standard deviations ABOVE the mean!! How rare is that? If we looked at our graph of a normal distribution below, we can see that going out just two standard deviations from the mean on each side covers at least 95% of the distribution. Our score puts us past that, into the less than 5% area in the tails of the distribution (and since we are looking only toward one tail that indicates even a smaller percent of people who did as well as we did).

Types of T-Test

1. One-Sample

2. Dependent (Repeated_ Samples

3. Independent Samples

Essay Instructions: Answer the following questions:
1. Describe the rationale for utilizing probability concepts. Is there more than one type of probability? If so, describe the different types of probability.
2. Briefly discuss probability distributions. What is a normal distribution? Please provide a written example of how 'understanding distribution' can be an asset for any business project.
Your paper should reflect scholarly writing and current APA standards. Please include citations to support your ideas.

Essay Instructions: Describe how probability is used in Buisness. Describe how business uses normal distribution and it's benefits. Describe the usefullness of probability distributions on business today. Explain how such statistical devices can aid the businessman in making sound business decisions.