Assignment:
In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 30 mpg and a standard deviation of 1.0 mpg. Suppose that the car manufacturer samples 5 cars from its assembly line and test them for mileage ratings.
- What is the distribution of the mean mpg for the sample?
- What is the probability that the sample mean will be greater than 31 mpg?
- What is the probability that the sample mean will be Jess than 29.5 mpg?
Provide complete and step by step solution for the question and show calculations and use formulas.