Declining availability of industrial land and shifting consumer demands are driving the average warehouse clear heights (how high the warehouse ceiling is from floor 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? b) 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? c) Canadian Building Corporation also reveals that the clear height for a warehouse in Burlington is expected to be uniformly distributed between 20 and 40 feet. A warehouse 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? i ) Given that Y is a normal random variable, the variable Z= (Y - 10) is also normally distributed. 1i 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. 111 Given that Z is a standard normal random variable, the value of Z is 0.86 if the area to the right of Z 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