Declining availability of industrial land and shifting consumer demands are driving the average warehouse clear heights (how high the warehouse ceiling is from oor to ceiling) to new levels. Canadian Building Corporation investigated and reported that the mean clear height for a warehouse in Hamilton is 30 feet. Suppose the clear heights are normally distributed and the standard deviation is 5 feet. a) A warehouse in Hamilton is randomly selected. What is the probability that the clear height is between 25.25 and 34.45 feet?I 11) Suppose the population standard deviation is unknown but the mean clear height is still 30 feet. If 99.42% of all Hamilton warehouses have a clear height greater than 24 feet, what is the population standard deviation? o) Canadian Building Corporation also reveals that the clear height for a warehouse in Burlincrton is ex ected to be uniforml distributed between 20 and 40 feet. A warehouse a: P Y is randomly selected. What is the probability that the clear height is at least 29.50 feet? d) This part is independent of parts a) to c). Which statement is not true '7 i) Giv en that Y is a normal landom variable the v ariable Z: (Y 10) is also normally distributed. ii) A graph. formula, or table that shows all possible values a random variable can assume. together with their associated probabilities. is called an expected value of a discrete random variable. iii) Given that Z is a standard normal random variable. the value on is 0.86 if the area to the right on is 0.1949. iv) In the normal distribution, the total area beneath the curve represents the probability for all possible outcomes for a given event