ADM2303Fall 2015Assignment #4 (19 Marks)Question 1. (4 points) With the upcoming holiday season, the national postal corporation uses anautomated sorter which scans postal codes in order to separate letters sent by mail. However in somecases, the scanner misclassifies letters and a manual inspection is also undertaken in order to ensurequality control standards are met. The management team is concerned that with the hiring of newemployees for the holiday period, the speed of the conveyor belt may not provide enough time for theinspectors to determine which letters are misclassified. In the following table, data from an experiment inwhich the same batch of letters (with known number of misclassified letters) was inspected usingdifferent conveyor belt speeds.Conveyor speed(ft/min)1012151720222528303235No. of misclassifiedletters found2721191413151211976a) (1 point) Using MINITAB, plot a scatterplot with the conveyor speed on the x-axis.b) (1 point) What does the scatterplot found in (a) indicate about the relationship between the twovariables?c) (2 points) Use MINITAB to calculate the correlation coefficient between the two variables. Interpretthe result. Does the management team’s concern seem justified?Question 2.(4 points) A manager of a restaurant in a commercial building would like to offer a new teadrink to customers. She randomly polled 100 customers and asked how many of them drink tea on aregular basis. Of the 100 customers, 41 reported to be tea drinkers.a) (1 point) Calculate , ̂the estimate of the true population proportion of customers who drink tea.b) (3 points) Before the poll was conducted, the manager believed that 52% of customers were teadrinkers. Assuming this assertion is true, find ܲ(.)14.0 ≤ ̂1Sections A to GADM2303Fall 2015Question 3. (6 Points) The inorganic mercury content in a single cigarette of a particular brand is arandom variable with mean 25 ng and a population standard deviation of 12 ng. A random sample of n =100 cigarettes is taken for analysis.തa) (2 points) What is the approximate distribution of the sample mean ܺ?b) (2 points) The inorganic mercury content for a cigarette is considered high when the content is greaterthan 29 ng. What is the probability that the resulting sample mean content will be greater than 29 ng?c) (2 points) Now suppose that the market analyst would like to test another brand of cigarettes andselects a random sample of ݊ = 25 cigarettes from a population with mean inorganic mercury content 25ng, but the standard deviation is now estimated from the sample as 10 ng. What is the probability that thesample mean content will be greater than 29 mg for this brand?Question 4. (5 Points) Using MINITAB, generate observations from an Exponential (λ=1) distribution.Generate 200 samples of 30 observations each by generating 200 rows of data and storing the results incolumns C1-C30. Refer to the MINITAB Instructions provided at the end of the assignment.i) Now, to simulate a random sample of size n = 3, select data from columns C1 – C3. Find the mean rowwise and store the result in column C31.ii) Similarly, simulate a random sample of size n = 10 by selecting data from columns C1-C10. Find themean row-wise and store the result in column C32.iii) Finally, simulate a random sample of size n = 30 by selecting data from columns C1-C30. Find themean row-wise and store the result in column C33.Submit responses to the following two questions with your assignment:a) (4 points) Plot a histogram of the sample means obtained in each of i), ii) and iii), and describe theshape of the distribution for each case. What do you notice as the sample size increases?b) (1 point) What theoretical result is illustrated by this procedure?