Please show your work! 1) A physical fitness association is including the mile run in its secondary -school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 373 seconds. 2) Suppose a store has a filling machine that fills 12 ounce bottles of juice. It is known that the amount of juice poured by this lling machine follows a normal distribution with a mean of 12.18 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more than 12.13 ounces of juice. 3) Suppose a store has a filling machine that fills 12 ounce bottles of juice. It is known that the amount of juice poured by this filling machine follows a normal distribution with a mean of 12.10 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.09 and 12.12 ounces. 4) Imagine your friend is usually up late, but has come on time before. Suppose your friend could be on time or up to 30 minutes late, with all intervals of time equally likely. a. What is the probability your friend will be between 10.23 and 20.14 minutes late? b. What is the probability your friend will be more than 15 minutes late given that they called and said they will be at least 7 minutes late because of trafc