# Questions dealing with concepts and distributions

Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

What is a z score and how could calculating a z help you in a business situation?

How does a box plot relate to the normal distribution? In what ways are they similar? In what ways are they different?

When working with the normal distribution to find probabilities, we often have to subtract the probability value that we found in the table from .5. Why do we do this? What is a good way to remember when to subtract from .5 or not?

Some teachers grade on a curve using the normal distribution to even out the scores. What do you think of this practice?

Â© BrainMass Inc. brainmass.com December 15, 2022, 8:16 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/questions-dealing-with-concepts-and-distributions-287283

#### Solution Preview

Dear Student,

The answers are in the attached document Answers.doc

They are also given below.

____________________________________________________________________________________________________

1. Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

The normal distribution is a commonly occurring distribution in nature and

many random phenomenon roughly approximate this distribution. For example,

1. Modern portfolio theory for stock returns, assumes that the return on a diversified asset portfolio follows a normal distribution. You can thus assume normal distribution and calculate the probability that your return will be greater than a certain value.

2. Distribution of IQ scores can be modeled using a normal distribution. If you want to calculate the probability that a random person in the population has a high IQ (say > 150), you can use the normal distribution table.

2. What is a z score and how could calculating a z help you in a business situation?

In statistics, a standard score indicates how many standard deviations an observation or datum is above or below the mean. It is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing. Standard scores are also called z-scores.

As one of the common indicators used to measure the stability of a ...

#### Solution Summary

Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

What is a z score and how could calculating a z help you in a business situation?