Understanding Standard Normal Distribution

The video tutorial explains how to find a z-score, c, in a standard normal distribution such that the probability of z being greater than c is 0.316. It covers the use of the cumulative z-score table to find the probability to the left of the z-score and calculates the z-score as approximately 0.48. The tutorial emphasizes understanding the areas under the normal distribution curve and how to interpret them using the z-score table.

What is the probability that a randomly selected data value has a z-score greater than c?

• 0.048

• 0.5

• 0.316

• 0.684

In a standard normal distribution, what percentage of data lies below z = 0?

• 50%

• 75%

• 25%

• 100%

Why is the z-score positive when finding the probability that z is greater than c?

• Because the area is exactly 0.5

• Because the area is less than 0.5

• Because the area is more than 0.5

• Because the area is negative

What does the cumulative z-score table provide?

• The total area under the curve

• The area to the right of the z-score

• The area to the left of the z-score

• The exact z-score value

How do you find the left-side probability if the right-side probability is 0.316?

• Divide 0.316 by 2

• Multiply 0.316 by 2

• Subtract 0.316 from 1

• Add 0.316 to 1

What is the approximate z-score 'c' found using the cumulative z-score table?

• 0.48

• 0.316

• 0.684

• 0.048

What is the probability of z being less than the z-score 'c' found?

• 0.048

• 0.316

• 0.684

• 0.5

What is the total area under the standard normal distribution curve?

• 0.316

• 2

• 1

• 0.5

What is the probability of z being greater than 0.48?

• 0.5

• 0.048

• 0.684

• 0.316

What does the area under the curve to the left of a z-score represent?

• The probability of z being less than the z-score

• The probability of z being equal to the z-score

• The probability of z being greater than the z-score

• The probability of z being not equal to the z-score