MIDTERM EXAMNATION 1. A Engr. Juan dela Cruz is in-charged of ensuring the quality of products and services produced by their beverage company located in Southern Luzon. One of their products is bottled cranberry juice. He observed that the amount of juice drink in each 32 ml bottle is actually a normally distributed random variable, with a mean of 32.2 ml and a standard deviation of 0.3 mL. a) Find the probability that, if a customer buys one bottle will contain less than 32 ml. b) Find the probability that, if a customer buys a cartoon of four bottles, the mean of the four will be less than that of 32 mL 2. A survey on the consumers buying behavior on shopping at Malls in a certain City showed that 30% use credits cards to make payment. In one of the footwear stores in this Mall, 20 customers were recorded to have purchased footwear items. a) Using Table of Appendix B, find the probability that at least 12 of the customers used credit cards. ) What is the probability that at least 3 customers, but not more than 6, used credit cards? c) What is the expected number of customers who used credit cards? d) Find the probability that exactly 14 customers did not use credit cards. e) Find the probability that at least 9 customers did not use credit cards