Question

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

What is the distribution of X? X ~ N( , ) ______

What is the distribution of x¯? x¯ ~ N( , ) ______

If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2. _____

For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2. 4. _____

4. The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.2 mm. Suppose that 17 individuals are randomly chosen. Round all answers to 4 decimal places where possible.

What is the distribution of x¯? x¯ ~ N( , ) _____

For the group of 17, find the probability that the average hand length is more than 187. ____

Find the third quartile for the average adult male hand length for this sample size. ______

Answer 1