Understanding Z-Scores and Probability with TI-84

The video tutorial explains how to find a Z-score (C) for a standard normal distribution where the probability of Z being greater than C is 0.316. It uses the TI-84 graphing calculator to demonstrate the process, emphasizing the need to input the probability to the left of the Z-score. The tutorial covers the concept of areas under the curve, the use of the inverse norm command, and provides step-by-step instructions for calculating the Z-score, which is approximately 0.4789.

What is the goal when finding a Z-score in a standard normal distribution?

• To calculate the standard deviation

• To find the mean of the distribution

• To determine the probability of Z being less than a certain value

• To find a value C such that the probability of Z being greater than C is given

Why is the Z-score positive when the area to the right is less than 0.5?

• Because the mean is always positive

• Because the standard deviation is negative

• Because the area to the right is always greater than 0.5

• Because the area to the right being less than 0.5 indicates a positive Z-score

What must be entered into the TI-84 calculator's inverse norm command?

• The probability to the right

• The probability to the left

• The Z-score directly

• The mean and standard deviation

How do you convert the probability to the right into the probability to the left?

• Subtract the probability to the right from 1

• Add the probability to the right to 1

• Divide the probability to the right by 2

• Multiply the probability to the right by 2

Which command on the TI-84 calculator is used to find the Z-score?

• Standard Deviation

• Mean Calculation

• Inverse Norm

• Normal CDF

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

• 0.5

• 0.316

• 1

• 2

What is the default mean and standard deviation used by the TI-84 when they are not specified?

• Mean = 0, Standard Deviation = 0

• Mean = 0, Standard Deviation = 1

• Mean = 1, Standard Deviation = 0

• Mean = 1, Standard Deviation = 1

What is the Z-score found using the TI-84 calculator for the given probability?

• 0.316

• 0.684

• 1.0

• 0.4789

What does a Z-score of 0.4789 indicate about the probability of Z being greater than this value?

• The probability is 0.684

• The probability is 0.316

• The probability is 0.5

• The probability is 1.0

What is the significance of rounding the Z-score to four decimal places?

• It increases the probability

• It is required by the calculator

• It ensures precision in calculations

• It decreases the probability