Understanding Normal Distribution and Z-Scores

The video tutorial explains the distribution of resting pulse rates among students at Santa Maria High School, which follows a normal distribution with a mean of 80 beats per minute and a standard deviation of 9 beats per minute. The school nurse plans to screen students whose pulse rates are in the top 30%. The tutorial guides viewers through using a Z-table to determine the minimum pulse rate for additional screening, resulting in a threshold of 85 beats per minute.

What is the mean resting pulse rate of students at Santa Maria High School?

• 70 beats per minute

• 80 beats per minute

• 90 beats per minute

• 100 beats per minute

What is the standard deviation of the resting pulse rates at Santa Maria High School?

• 11 beats per minute

• 9 beats per minute

• 7 beats per minute

• 5 beats per minute

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

• 95%

• 99%

• 68%

• 50%

What is the pulse rate value one standard deviation above the mean?

• 89 beats per minute

• 98 beats per minute

• 80 beats per minute

• 71 beats per minute

What percentage of students are targeted for additional screening based on their pulse rates?

• 40%

• 10%

• 20%

• 30%

What is the z-score for the top 30% of the distribution?

• 0.63

• 0.73

• 0.43

• 0.53

How do you calculate the actual pulse rate from a z-score?

• Subtract the z-score from the mean

• Multiply the z-score by the mean

• Add the z-score to the mean

• Multiply the z-score by the standard deviation and add to the mean

What is the calculated pulse rate for the top 30% threshold before rounding?

• 85.7 beats per minute

• 84.7 beats per minute

• 83.7 beats per minute

• 82.5 beats per minute

To what value is the calculated pulse rate rounded?

• 83 beats per minute

• 84 beats per minute

• 85 beats per minute

• 86 beats per minute

What is the significance of a pulse rate of 85 beats per minute in this context?

• It is the average pulse rate

• It is the minimum threshold for additional screening

• It is the maximum pulse rate recorded

• It is the pulse rate of the healthiest students