A= 9 B=8

9:19 PM Mon Feb 7 d2l.nlc.bc.ca + AutomaticZoom Please note that most questions are personalized, where a is the last digit of your student number and b is the third last digit of your student number. For example, if your student number is 0012345, then a = 5 and b = 3. MATH104RO/MGMT290RO Assignment #6 Following Unit 3 in the manual. 1. [5 points] Let as be the weight of a randomly selected man. According to the text, a: is normally distributed with the mean of 172 + (1 pounds and the standard deviation of 29 1) pounds. Find each of the following. (a) Sketch the PDF (Probability Density function) of 2:. Label the mean. (b) Find the probability that a randomly selected man has a weight between 170 pounds and 180 pounds. (c) Let E be the random variable measuring the sample mean weight of 100 randomly select men. Is the random variable E normally distributed; Why? Find the mean and the standard deviation of E. Find the probability that randomly selected 100 men have an average weight between 170 pounds and 180 pounds. Interpret your answer in terms of a relative frequency. Sketch the PDF of E using the same scale as that of as. Label the mean of E. 2. [5 points] The probability of an egg being accidentally cracked because of excessive jostling during transport to the retailer is 0.05 + 0.001 X a. The retailer opens a random sample of 120 + 17 eggs and carefully checks each one for cracks. Let a: be the random variable that counts the number of cracked eggs in the sample. Does a: yield a binomial probability distribution? Why? Find the mean and standard deviation of as. Can we use Possion distribution to approximate the binomial distribution? Why? Use the Possion distribution formula to approximate the probability that the sample contains exactly 8 cracked eggs. Can we use normal distribution to approximate the binomial distribution? Why? Use a normal distribution to approximate the probability that the sample contains exactly 8 cracked eggs. Use a normal distribution to approximate the probability that the sample contains at least 8 cracked eggs