Question

Suppose the volume of gasoline sold on a weekday at a local gas station is known to be normally distributed with mean 12,000 gallons and standard deviation 1000 gallons. In addition, the volumes sold on different days are independent random variables.

1. What is the probability distribution of the average volume sold over four weekdays? (Provide the distribution name and all parameter values.)

2. What is the probability that the average volume sold over four weekdays is more than 12,400 gallons?

3. Suppose gasoline sells for $3.20/gallon on Monday and $2.40/gallon on Tuesday. What is the probability that the combined revenue from Monday and Tuesday exceeds $60,000? (Note: You should assume revenue is a continuous random variable even though a reasonable interpretation might conclude that fractions of a cent are not allowable.)

Answer 1