Understanding Normal Distribution and the Empirical Rule

The video tutorial explains a company's policy on retiring fleet cars based on a normal distribution of months in service. It introduces the concept of normal distribution, detailing the mean and standard deviation. The empirical rule (68-95-99.7 rule) is applied to determine the percentage of cars in service between 44 and 54 months. The tutorial also covers calculating z-scores to find probabilities and visualizes the standard normal distribution to reinforce understanding.

What is the mean number of months in service for the company's fleet cars?

• 5 months

• 39 months

• 54 months

• 44 months

What is the standard deviation of the company's fleet cars' months in service?

• 5 months

• 39 months

• 54 months

• 44 months

According to the empirical rule, what percentage of data falls within one standard deviation of the mean?

• 50%

• 68%

• 95%

• 99.7%

Which of the following is NOT a part of the empirical rule?

• 50%

• 68%

• 95%

• 99.7%

How many standard deviations above the mean is 44 months?

• 3

• 2

• 0

• 1

What percentage of cars remain in service between 44 and 54 months according to the empirical rule?

• 95%

• 68%

• 15.85%

• 99.7%

What is the z-score formula used to calculate the number of standard deviations a data point is from the mean?

• X / mean

• (mean - X) / standard deviation

• (X - mean) / standard deviation

• mean / X

What does a z-score of 1 indicate about a data point?

• It is one standard deviation below the mean

• It is one standard deviation above the mean

• It is at the mean

• It is three standard deviations above the mean

What is the z-score for 54 months?

• 3

• 1

• 0

• 2

What is the purpose of using z-scores in this context?

• To determine the mode

• To calculate the mean

• To determine how many standard deviations a data point is from the mean

• To find the median