A particular fruits weights are normally distributed

opic: 9 math probelms Number of Pages: 1 (Double Spaced) Number of sources: 1 Writing Style: APA Type of document: Math Problem Academic Level:High School Category: Mathematics Language Style: English (U.S.) Order Instructions: ATTACHED 1. On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 481 pounds and a standard deviation of 80 pounds. The cow transport truck holds 12 cows and can hold a maximum weight of 6468. If 12 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 6468? (This is the same as asking what is the probability that their mean weight is over 539.)(Give answer correct to at least three decimal places.) question 2 : A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 202.5-cm and a standard deviation of 1.2-cm. Find the probability that the length of a randomly selected steel rod is between 199.7-cm and 201.2-cm. P(199.7-cm < X < 201.2-cm) = Question 3 :A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 144.1-cm and a standard deviation of 1.2-cm. Find the probability that the length of a randomly selected steel rod is less than 144.2-cm. P(X < 144.2-cm) = Question 4 :Let X represent the full height of certain species of tree. Assume that X is normally distributed with a mean of 226.5 feet and a standard deviation of 19.9 feet. Find the probability that the full height of a randomly selected tree is less than 194.7 feet. P(X<194.7)= Question 5 :A particular fruit's weights are normally distributed, with a mean of 767 grams and a standard deviation of 36 grams. If you pick 23 fruit at random, what is the probability that their mean weight will be between 749 grams and 771 grams Question 6 :An electronic product takes an average of 5 hours to move through an assembly line. If the standard deviation of 0.3 hours, what is the probability that an item will take between 4.1 and 4.6 hours to move through the assembly line? Question 7 :A manufacturer knows that their items have a normally distributed lifespan, with a mean of 15 years, and standard deviation of 4.8 years. If you randomly purchase 4 items, what is the probability that their mean life will be longer than 13 years? Question 8: NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem. The population of weights for men attending a local health club is normally distributed with a mean of 185-lbs and a standard deviation of 25-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6860-lbs. Assume that there are 35 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded? average weight = What is the probability that one randomly selected male health club member will exceed this weight? P(one man exceeds) = If we assume that 35 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded? P(elevator overloaded) If the elevator is full (on average) 3 times a day, how many times will the elevator be overloaded in one (non-leap) year? number of times overloaded Question 9 :A particular fruit's weights are normally distributed, with a mean of 265 grams and a standard deviation of 6 grams. If you pick 15 fruits at random, then 4% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram. Question 10 :A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.4 years, and standard deviation of 1.1 years. If 11 items are picked at random, 7% of the time their mean life will be less than how many years? Give your answer to one decimal place.