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.

d) Suppose now that µ is unknown. A random sample of 9 measurements gives
x¯ = 35 m/s. Calculate a 93.8% confidence interval. How likely is it that µ lies
outside this interval?

e) A random sample of 9 measurements gives ¯x = 35 m/s. Perform a two-tailed
hypothesis test (with confidence level 93.8% ) to test the claim that µ = 32.2 m/s.

f) Suppose that both µ and σ are unknown now. A random sample of 9 measurements gives ¯x = 35 m/s and s = 1.67 m/s. Perform a two-tailed hypothesis
test (with confidence level 93.8% ) to test the claim that µ = 32.2 m/s.

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) Suppose now that μ is unknown. A random sample of 9 measurements gives x ̄ = 35 m/s. Calculate a 93.8% confidence interval. How likely is it that μ lies outside this interval?

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.

B) Find z so that 93.8% of the area under the standard normal curve lies between −z and z.  

Note: this is equals to 0.092

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

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) Suppose now that μ is unknown. A random sample of 9 measurements gives x ̄ = 35 m/s. Calculate a 93.8% confidence interval. How likely is it that μ lies outside this interval?

b) A random sample of 9 measurements gives x ̄ = 35 m/s. Perform a two-tailed hypothesis test (with confidence level 93.8% ) to test the claim that μ = 32.2 m/s.

c) Suppose that both μ and σ are unknown now. A random sample of 9 mea- surements gives x ̄ = 35 m/s and s = 1.67 m/s. Perform a two-tailed hypothesis test (with confidence level 93.8% ) to test the claim that μ = 32.2 m/s.