Understanding Normal Distribution and Z-Scores

This video tutorial covers the normal distribution, focusing on standard scores or z-scores, the standard normal distribution, and how to determine probabilities using the TI-84 calculator. It explains the empirical rule and provides examples of calculating z-scores and data values. The tutorial also demonstrates using the TI-84 calculator to find probabilities and areas under the normal distribution curve.

What does the empirical rule state about data within one standard deviation of the mean?

• Approximately 50% of data falls within one standard deviation.

• Approximately 68% of data falls within one standard deviation.

• Approximately 95% of data falls within one standard deviation.

• Approximately 99.7% of data falls within one standard deviation.

What is the mean and standard deviation of the standard normal distribution?

• Mean is 1, standard deviation is 0

• Mean is 0, standard deviation is 1

• Mean is 0, standard deviation is 0

• Mean is 1, standard deviation is 1

How do you calculate a z-score for a data value?

• Multiply the data value by the mean and divide by the standard deviation

• Subtract the mean from the data value and divide by the standard deviation

• Add the mean to the data value and divide by the standard deviation

• Subtract the standard deviation from the data value and divide by the mean

If a z-score is negative, what does it indicate about the data value?

• The data value is equal to the mean

• The data value is below the mean

• The data value is at the maximum

• The data value is above the mean

What is the z-score for a data value of 26, given a mean of 22 and a standard deviation of 5?

• 0.8

• 1.6

• 0.4

• 1.2

Which function on the TI-84 calculator is used to find the area under the normal distribution curve?

• normalcdf

• normalpdf

• binomcdf

• invNorm

What is the area to the left of the mean in a normal distribution?

• 0.75

• 1.0

• 0.5

• 0.25

How do you find the probability of a data value being less than a certain number using the TI-84?

• Use the binomcdf function

• Use the invNorm function

• Use the normalcdf function with a negative lower bound

• Use the normalpdf function

What is the probability of spending more than six days in recovery if the mean is six days?

• 75%

• 50%

• 100%

• 25%

If 500 patients undergo a procedure, how many are expected to recover between five and seven days?

• 234 patients

• 250 patients

• 350 patients

• 300 patients