Exploring Normal Distribution Concepts

What does a Z-score represent in a data set?

• The highest value in the data set

• The average value of the data set

• The position of a particular value within the data set

• The middle value of the data set

Which of the following is an example of a discrete random variable?

• The weight of a newborn baby

• The number of heads in five coin tosses

• The time taken to run a marathon

• The height of students in a class

Why can't the number of babies born in a hospital be considered a continuous variable?

• Because it can only take on fixed values

• Because it can take on any real value

• Because it is measured over a range

• Because it is not a measurable quantity

What shape does a normal distribution curve typically have?

• A U shape

• A straight line

• A bell shape

• A zigzag pattern

According to the empirical rule, what percentage of data falls within one standard deviation of the mean in a normal distribution?

• 68%

• 50%

• 99.7%

• 95%

What is the empirical rule also known as?

• The 68-95-99.7 rule

• The 50-50 rule

• The normal curve rule

• The standard deviation rule

Why might using a normal curve for grading be problematic?

• It ensures everyone gets the same grade

• It can result in unfair competition among students

• It makes grading easier for teachers

• It does not account for individual performance

In a normal distribution, what percentage of data falls within three standard deviations of the mean?

• 100%

• 99.7%

• 95%

• 68%

What is the purpose of using a Z-score table?

• To find the mean of a data set

• To determine the standard deviation

• To find the area under the curve for different Z-scores

• To calculate the median

If a Z-score is 1, what percentage of data lies to the left of this Z-score in a normal distribution?

• 84%

• 68%

• 50%

• 95%