Chapter 8 Continuous Random Variables

Question 1

Continuous Random Variable

Answer 1

a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.

Question 2

Normal distribution

Answer 2

also known as the Gaussian or standard normal distribution, is the probability distribution that plots all of its values in a symmetrical fashion, and most of the results are situated around the probability’s mean. Values are equally likely to plot either above or below the mean.

Question 3

Standard normal distribution

Answer 3

. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Question 4

Z- Values, and formula

Answer 4

The values on a standard normal distribution. The formula is (z equals X value minus mean, divided by standard deviation). This process standardizes the distribution.

Question 5

In terms of linearly transforming data, how does a distribution shift when it is standardized?

Answer 5

Our resulting distribution will not change in shape, and the values will have the same relation to one another.

Question 6

Can you turn any distribution into a standard normal one?

Answer 6

No, only normal distributions can be transformed into standard normal distributions. No such thing as ‘normalizing’ a distribution by turning into a standard normal.

Question 7

What is standard deviation in a standard normal distribution?

Answer 7

Always equal to 1

Question 8

Mean median and mode in standard normal distribution? What does this imply for probabilities?

Answer 8

Zero. Thus,50th percentile is at 0 so 0.50 prob of obtaining value great than 0 or less than 0.