Mathematics Homework Help

Some candy is packed in polythene bags with nominal weight 175 g. The weight (in g) of a random bag is measured by a random variable X with probability density function:

Assume the weights of different bags of candy are independent.

1. Find the constant a. If you are unable to find a, then make an educated guess, so that you can continue with solving the present problem.
2. What is the interquartile distance of X?
3. What is P[X=175], the probability that a random bag of candy has the nominal weight?
4. Calculate E[X|X≥175], the expected weight of a random bag of candy when it is known that this bag has at least the nominal weight.
5. The manufacturer sells the candy in cardboard boxes with 40 random candy bags. What is the probability that more than 75% of the candy bags in a random box weigh more than the nominal weight?
6. A grocer sorts random bags of candy. What is the probability that he must inspect at least 14 bags and less than 18 bags until he finds the 12th bag weighing more than the nominal weight final answer is not sufficient, calculation must include description of random variables, mentioning the applied mathematical property and why it holds, answer should be atleast 4 significant figures.