. A study in Batu Pahat General Hospital's on patient account division has compiled data on the age of accounts receivables. The data collected indicates that the age of the accounts follows a normal distribution with mean 28 days and a standard deviation of 8 days. Ahmad would like to know the probability of the accounts between 20 and 40 days old and the probability of the accounts which less than 30 days old. Shows the calculation of both problems. (7 marks) . The length of time for longdistance telephone calls from Malaysia to Thailand has a mean of 16 minutes and a standard deviation of 4 minutes. Suppose a sample of 35 telephone calls is used to reflect on the population of all long- distance calls. Calculate the chance that the average of the 35 telephone calls is between 17 and 18 minutes. (8 marks) . Bella's aims to construct a confidence interval for the mean of a normal population with known standard deviation. List three factors that could help her in reducing the size of the margin error. Then, she collects a random sample of size from a population and from the data collected she compute a 95% confidence interval for the mean of the population. Based on the same dataset, state one factor that could produce a new confidence interval with a larger width (Hint: Larger margin of error). (5 marks) . A random sample of thirty firms dealing in wireless products was selected to determine the proportion of such firms that have implemented new software to improve productivity. It turned out that eight of the thirty have implemented such software. Compute a 95% confidence interval on p, the true proportion of such firms that have implemented new software. In other situation, suppose there is concern about whether or not the point estimate of p = 8/30 is accurate enough because the confidence interval around p is not sufficiently narrow. By using p as your estimate of p, calculate how many companies would need to be sampled to have a 95% confidence interval with a width of only 0.05. (10 marks) Aminah wishes to perform the hypothesis testing versus with. The sample size 25 was obtained independently from a population with standard deviation