Question

The Normal Probability Distribution In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean (u) zero and variance (σ2) one (and standard deviation of

1). What is a z score?

2. What is the purpose of a z score?

3. If a z score were -3, where on the graph would it be? Is this a rare or a common score? Why? One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook.

4. According to the table, what is the probability when z ≤ -1.23? The probability when z ≤ 1.23? 5. Select two other pairs of "opposites" on the z table (like 2, -2 etc.) and give their probabilities. 6. Show the math of adding each of the pairs. What is the total each time? Why is that the total? 7. What are the properties of the Standard Normal Probability Distribution?

Answer 1

Dear student, we can provide you with a solution of 4 subquestions at a time.

1) A z-score is the number of standard deviations from the mean a data point is. It's a measure of how many standard deviations below or above the population mean a raw score is.

2) The standard score is a very useful statistic because it allows us to calculate the probability of a score occurring within our normal distribution and it enables us to compare two scores that are from different normal distributions.

3)

This is a rare score, as the score corresponding to this is 3 standard deviations below the mean.

4)