Question 1 The number of people visiting the University of Dar es Salaam Website per day is normally distributed with a mean of 700 and a standard deviation of 120. Required i) Determine the proportion of days with more than 700 visits per day ii) Determine the proportion of days with between 730 and 820 visits per day iii) Find the number of visits per day such that 5% of days have the number of visits below this number.
Question 2 The Jema Kitchenware Company located in China ships large consignments of ceramic cups to a large buyer in Tanzania. When the Jema manufacturing process is working correctly, which is 90%, the proportion of defective cups is approximated 10 percent. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 50%. Required: If a defective cup is found, what is the probability that the process is functioning correctly?
Question 3 Jema is a leading wholesale supplier of shoes located in Kariakoo. Jema takes orders from its customers by phone or email. After receiving orders, a staff is assigned to prepared the order. It takes an average of 6 minutes with a standard deviation of 2.5 minutes to process phone orders. Moreover, the time it takes for a shipping arrangement to be completed is normally distributed with a mean of 35 minutes and a standard deviation of 8.6 Required i) What is the probability that a well experience Jema staff will take at most 2.93 minutes to process an order? ii) What is the probability than an inexperienced staff with take at least 8.23 minutes an
