6. An airline data shows that the weight of baggage of passenger is normally distributed. It is found that the mean weight of baggage (u) is 12kg and the standard deviation (o) is 2.5kg. a) Find the probability that the weight of baggage is more than 16kg. (5 marks) b) The airline company set a new policy that top 15% baggage weight is required for extra charge. Determine the weight of baggage that is required for extra charge. (4 marks) c) If a sample of 15 baggage is chosen at random, find the probability that at least one would has weight more than 16kg. (Hints: Use Binomial to solve it) (6 marks)

Nick has collected data to find that the body weights of the forty students in a class has a normal distribution. What is the probability that a randomly selected student has a body weight of greater than 169 pounds if the mean is 142 pounds and the standard deviation is 9 pounds? Use the empirical rule. Provide the final answer as a percent rounded to two decimal places.

Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 80% of the students who took the test. Tom takes the test and scores 595. Will he be admitted to this university?

For a population that has a standard deviation of 22​, figure the standard deviation of the distribution of means for samples of size​ (a)2​, (b)4​, (c)5​ and​ (d)10.