Continuous Random Variables and Normal Distribution

Questions and Answers

What is a continuous random variable?

A continuous random variable is normally distributed if its relative frequency histogram has the shape of a normal curve.

What are the two types of continuous random variables?

Normal distribution (correct)

Discrete distribution

Uniform distribution (correct)

Binomial distribution

What happens to the graph of the normal curve as the mean increases?

The graph slides right.

What happens to the graph of the normal curve as the standard deviation decreases?

The graph compresses and becomes steeper. Signup and view all the answers

What are inflection points in relation to the normal curve?

Inflection points are where the curve changes concavity, typically occurring at μ−σ and μ+σ. Signup and view all the answers

Which of the following are properties of the normal curve? (Select all that apply)

The area under the normal curve to the right of the mean is 0.5. Signup and view all the answers

How can the area under a normal curve be interpreted? (Select all that apply)

It corresponds to the probability that a randomly selected individual has the characteristic. Signup and view all the answers

The area under the normal curve to the right of μ equals ______.

1/2 Signup and view all the answers

What is the probability that a friend is between 25 and 30 minutes late if considering a uniform probability density function?

.167 Signup and view all the answers

If it is 10 A.M., there is a 10% probability the friend will arrive within how many minutes?

3 minutes Signup and view all the answers

In the report, what does it mean when researchers state results remain significant after adjustment for socioeconomic status?

The researchers accounted for potential lurking variables. Signup and view all the answers

What is an observational study?

It is when researchers observe individuals in the study without trying to influence an explanatory variable. Signup and view all the answers

Study Notes

Continuous Random Variables

Continuous random variable is normally distributed if its relative frequency histogram resembles a normal curve.
There are two types of continuous random variables: uniform distribution and normal distribution.

Normal Curve Characteristics

As the mean increases, the normal curve graph shifts to the right.
A decrease in standard deviation causes the normal curve to compress and become steeper.
Key points on a normal curve include inflection points, which occur at μ−σ and μ+σ.

Properties of the Normal Curve

The highest point of the curve is at the mean value.
The normal curve exhibits symmetry around the mean.
The area under the normal curve to the right of the mean equals 0.5, indicating equal distribution.

Area Under the Normal Curve

The area can be interpreted as the probability of selecting an individual with a particular characteristic.
It also represents the proportion of the overall population possessing that characteristic.
The area to the right of the mean (μ) is always 1/2 of the total area.

Uniform Probability Density Function

Calculated probability of being between 25 and 30 minutes late is 16.7%.
There is a 10% probability the friend will arrive within 3 minutes, if it is 10 A.M.

Research Methodology

Researchers conducted an observational study, simply observing individuals without attempting to influence variables.
Adjustments for socioeconomic status imply the researchers accounted for confounding variables to enhance outcome credibility.

Description

Explore the concepts of continuous random variables, focusing on their normal distribution characteristics. This quiz covers key features of the normal curve, including its symmetry, the area under the curve, and the significance of mean and standard deviation. Test your understanding of these fundamental statistical concepts.