Standard Normal Distribution Concepts

The video tutorial covers the standard normal distribution, explaining its properties, approximation rules, and how to calculate probabilities using the standard normal table. It also discusses key identities and provides examples of solving advanced probability problems. The tutorial emphasizes the importance of understanding the standard normal table for foundational courses.

What is a standard normal distribution?

• A distribution with mean 0 and standard deviation 1

• A distribution with mean 1 and standard deviation 0

• A distribution with mean 1 and standard deviation 1

• A distribution with mean 0 and standard deviation 0

What shape does the standard normal curve have?

• Triangular

• Rectangular

• Flat

• Bell-shaped

What percentage of observations lie between -1 and 1 in a standard normal distribution?

• 50%

• 68%

• 95%

• 99.7%

If Z is a standard normal variable, what is the probability that Z is greater than 0?

• 1.0

• 0.75

• 0.5

• 0.25

Which identity is true for a standard normal distribution?

• P(Z < x) = 1 - P(Z > x)

• P(Z < x) = P(Z < -x)

• P(Z < x) = 1 - P(Z < x)

• P(Z < x) = P(Z > x)

What does a standard normal table provide?

• Standard deviation of any distribution

• Probabilities for any distribution

• Probabilities for a standard normal distribution

• Mean and variance of any distribution

How do you find the probability that Z is less than 2.2 using the standard normal table?

• Subtract 0.5 from the table value for Z = 2.2

• Multiply the table value for Z = 2.2 by 2

• Look up Z = 2.2 in the table

• Add 0.5 to the table value for Z = 2.2

If the probability that Z is greater than x is 0.05, what is the value of x?

• 0.95

• 2.58

• 1.96

• 1.65