This problem depends on the following set up. Suppose you have a closed container (heated to a fixed temperature) full of a specific gas. We fix a specific gas particle within the container and...

This problem depends on the following set up. Suppose you have a closed container (heated to a fixed temperature) full of a specific gas. We fix a specific gas particle within the container and measure its velocity as x m/s. The random variable x then follows a normal distribution with mean μ and σ = 5 m/s.

a) Find z so that 93.8% of the area under the standard normal curve lies between −z and z. Note: If you choose not to do this part of the problem, use a confindence level of 95% in parts d, e, and f.

b) Suppose that μ is 32.2 m/s. Find the percentage of time that the particle’s velocity is more that 35 m/s.

c) Again, suppose that μ is 32.2 m/s. Find the percentage of time that the average velocity of the particle is more that 35 m/s if you take 9 random measurements.