Assignment 2
1. What is the normal distribution/curve? What are the important properties of the standard normal curve? Why is the standard normal curve important to predicting values?
2. Define a z-score. What two pieces of information does this give you about the raw score?
3. A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45. If GPA is normally distributed, what percentage of the students has GPAs
Z score
Area
a.
less than 2.30
b.
less than 2.00
c.
more than 2.00
d.
more than 3.00
e.
between 2.50 and 3.50
f.
between 2.00 and 2.50
4. For the distribution of GPAs described in Question 3, what is the probability that a randomly selected student will have a GPA
Z score
Probability
a.
less than 3.40
b.
less than 3.78
c.
more than 3.50
d.
more than 2.50
e.
between 2.00 and 3.00
f.
between 3.00 and 3.50
5. A researcher wanted to learn something about the religious affiliation of the students at the local college (e.g., what percent were Catholic, Jewish, etc.). This information was not available from the Registrar and the researcher was working with a very limited budget. Therefore, she used the principle of EPSEM to select a group of 200 students, called each of them at home, and conducted a brief interview. She was able to develop many conclusions based on this information. For example, she found that 50 of the 200 respondents were Catholic and concluded that about 25% of students at the college would claim the same religious affiliation.
Identify each of the following elements in this research scenario and explain their importance:
a. Populationb. Samplec. Parameterd. Statistice. EPSEMf. Representative
Please submit your answers to the assignments folder via a word document by the end of the learning module. Assignments scoring above a 35% Turnitin.com rating are subject to a point reduction. Assignments scoring above a 50% Trunitin.com rating will receive a zero on the assignment for originality, not for plagiarism. Keep direct quotes to a minimum.
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What is the normal distribution/curve? What are the important properties of the standard normal curve? Why is the standard normal curve important to predicting values?
Introduction
The normal distribution is a curve that represents data. The standard normal curve is one example of how you can use the normal distribution to predict values. In this lesson, we will learn what the standard normal curve is and why it’s important in predicting values.
What is the normal distribution/curve?
The normal distribution is a common probability distribution that describes the behavior of random variables that take on a value between 0 and 1. The normal curve has its most commonly used values at 0 and -1, with a mean of zero and standard deviation of one.
The bell-shaped curve is symmetrical around its mean, so it doesn’t matter which point you draw on the graph–the area under it will be equal to half its height (the area under any point). The centerline runs from -∞ to +∞; anything less than or greater than this line cannot be considered part of this set because their areas don’t add up to 1.
What are the important properties of the standard normal curve?
The standard normal curve is a symmetric bell-shaped curve that has a mean of zero and a standard deviation of one. This means that on average, if you take the value at any point in time and plot it against itself, there will be no difference. The mean or average value is always zero while the standard deviation is always one (which makes sense since it’s based on your original data).
Why is the standard normal curve important to predicting values?
The standard normal curve is a good way to predict values because it is a common distribution. The standard normal curve has many uses in statistics and economics, but one of its most important applications is in predicting the mean, median and mode of data.
Because the standard normal distribution represents a common shape for data that have been collected from different sources (such as heights), it helps us make predictions about future observations–for example if we know someone’s height then we can use this information to predict their weight or age based on their age bracket.
The standard normal curve is useful in predicting values because it is a very common and well known distribution.
The standard normal curve is useful in predicting values because it is a very common and well known distribution. As mentioned above, this curve can be used for many applications. For example, the mean (average) of an entire population can be estimated using this function:
where μ(x) = mean and σ(x) = standard deviation. The standard deviation of any given population will vary from person to person but it does not have an exact value because there are too many factors that affect our measurements such as age, gender and weight etc.. This means that every individual has a slightly different average weight but within each group there will be similar amounts of variation between people’s weights due to variability across populations or groups.
Conclusion
The standard normal curve is a very common and well known distribution. It is also useful in predicting values because it allows us to make accurate predictions based on the data we have collected from our experiments.