Understanding Normal Distribution and Z-Scores

The video tutorial explains how to solve a problem using the TI-84 calculator by calculating the probability of light bulb replacement requests within a given range. It covers the concept of normal distribution, using the TI-84 to find probabilities, and an alternative method using Z-scores. The tutorial provides step-by-step instructions for both methods and highlights the accuracy of the calculator compared to the empirical rule.

What is the mean of the distribution of daily requests for light bulb replacements?

• 95

• 68

• 11

• 49

Which function on the TI-84 calculator is used to find the percentage of requests between two values?

• binomial CDF

• binomial PDF

• normal CDF

• normal PDF

What is the approximate percentage of requests between 16 and 49 according to the TI-84 calculator?

• 95.45%

• 49.87%

• 99.73%

• 68.27%

How does the result from the TI-84 calculator compare to the empirical rule?

• It is not comparable

• It is the same

• It is more accurate

• It is less accurate

What does a z-score indicate?

• The mean of the data

• The standard deviation of the data

• How many standard deviations a value is from the mean

• The probability of a value

What is the z-score for a request value of 16?

• -3

• 0

• 3

• -1

What is the z-score for a request value equal to the mean?

• 0

• 1

• -1

• 3

When using z-scores, what are the mean and standard deviation set to?

• Mean = 1, SD = 0

• Mean = 1, SD = 1

• Mean = 0, SD = 1

• Mean = 0, SD = 0

What is the lower z-score used in the TI-84 calculation for the probability between -3 and 0?

• -1

• 3

• -3

• 0

What is the final probability result when using z-scores on the TI-84?

• 49.87%

• 68.27%

• 95.45%

• 99.73%