5. The ventricle is the cavity in the brain. The mean volume of ventricles in the healthy elderly is 38.3 cm3. We know that the ventricular volume is normally distributed. To inspect the volume of ventricle as a biomarker for Alzheimer’s disease, we collected the ventricular volumes of 25 Alzheimer’s disease patients. If their sample mean was 49.9 cm3 with a sample
standard deviation of s=25.3 cm3. Can we conclude that the mean ventricular volume of Alzheimer’s disease patients is not equal to 38.3 cm3? Use the significance level of 5%.

You may use the online t-distribution calculator to solve the question:
 

Question 10 The weekly demand for a product approximately has a normal distribution with mean 1,000 and standard deviation 200. The current on hand inventory is 2,200 and no deliveries will be occurring in the next two weeks. Assuming that the demands in different weeks are independent,
a) What is the probability that the demand in each of the next 2 weeks is less than 1,100?
b) What is the probability that the total of the demands in the next 2 weeks exceeds 2,200?

4. In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 300 diodes.
(a) How many diodes would you expect to fail on a circuit board, and what is the standard deviation of the number that are expected to fail?
(b) With Poisson distribution approximation, what is the (approximate) probability that at least one diode will fail on a randomly selected board? Round your answer to 2 decimal places.
(c) If ten boards are shipped to a particular customer, how likely is it that at least two of them will work properly? (A board works properly only if all its diodes work)