PLEASE USE : A= 9 B= 8

7132 PM Mon Jan 31 '3' 100% - Assignment 5 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. MATH104A0/MGMT290AO Assignment #5 Following Unit 3 in the manual. 1. [3 points] The probability of an egg being accidentally cracked because of excessive jostling during transport to the retailer is 0.08 0.001 x a. The retailer opens a random sample of 120 b eggs and carefully checks each one for cracks. Let 1: be the random variable that counts the number of cracked eggs in the sample. a. Does a yield a binomial probability distribution? Why? b. Find the mean and standard deviation of :r. c. Can we use Possion distribution to approximate the binomial distribution? Why? . Use the Possion distribution formula to approximate the probability that the sample contains no cracked eggs. Round your answer to 6 decimal places. . Find the probability that the sample contains at least one cracked eggs. Round your answer to 6 decimal places. . Use the Possion distribution formula to approximate the probability that the sample contains at most 2 cracked eggs. Round your answer to 6 decimal places. 2. [2 points] Find the critical value z,l for the signicance level (1' = 0.05+0.01 x a. Show your work. 3. [5 points] Let .r be the random variable representing the LQ. score of a. randomly selected adult. Assume that .r is normally distributed with the mean of 100 e a and the standard deviation of 15 + 6. Find each of the following. (a) Sketch the PDF (Probability Density function) of 1'. Label the mean. (b) Find P(:r > 125). Represent this probability as an area. Interpret your answer in terms of a relative frequency. (c) Find P(85