Understanding Fuel Consumption and Probability

The video tutorial explains Shinji's fuel usage during his commute, which follows a normal distribution. It provides summary statistics for fuel usage to work and home, and combines these to calculate the total distribution for a round trip. The tutorial then calculates the variance and standard deviation for the round trip, and uses a Z-score to determine the probability of Shinji running out of fuel, which is 2.28%.

What type of distribution does Shinji's fuel usage follow for each part of his commute?

• Poisson distribution

• Exponential distribution

• Normal distribution

• Uniform distribution

What is the mean amount of fuel Shinji uses for his commute to work?

• 10 liters

• 12 liters

• 15 liters

• 8 liters

What is the standard deviation of fuel usage for Shinji's return trip home?

• 1.5 liters

• 2 liters

• 2.5 liters

• 3 liters

How do you calculate the variance of the combined trip?

• Add the means of both trips

• Multiply the standard deviations

• Subtract the variances of both trips

• Add the variances of both trips

What is the variance of the round trip fuel usage?

• 7.25

• 5.25

• 6.25

• 4.25

What is the Z-score for Shinji's fuel usage if he uses 25 liters?

• 2

• 1.5

• 1

• 2.5

What does a Z-score of 2 indicate in terms of standard deviations?

• 4 standard deviations above the mean

• 3 standard deviations above the mean

• 2 standard deviations above the mean

• 1 standard deviation above the mean

What is the probability that Shinji runs out of fuel?

• 1.28%

• 2.28%

• 3.28%

• 4.28%

How is the probability of running out of fuel calculated?

• By adding the Z-score to the mean

• By subtracting the cumulative area from 1

• By multiplying the Z-score by the standard deviation

• By dividing the mean by the standard deviation

What is the cumulative area below two standard deviations above the mean?

• 0.9772

• 0.9272

• 0.8772

• 0.9972