Course: Introduction to Statistics (Bus-172) Answer all the questions. Question: 1 A company recently installed a new photocopy machine and evaluating how long it takes for new workers to learn how to use the machine. Suppose it is known that the learning times for all new workers have a skewed-to-the-right distribution with mean 90 minutes and standard deviation of 7 minutes. A sample of 36 workers are Selected. (a) What is the probability that the mean learning time of those sample of 36 workers is at least 98 minutes? (b)What type of shape did you assume for the sampling distribution for sample mean and on what ground? Justify your answer. (c) if one worker starts to learn using the machine at 12 in the noon and the lunch time is 1:40pm, what is the probability that the worker will finish learning before lunch time. (d) Show both the population distribution and sampling distribution of sample mean in a single graph. Question: 2 Seventy percent of the adults in Bangladesh favor some kind of government control on the prices of medicines. Assume that this percentage is true for the current population of all adults. Let p be the proportion of adults in a random sample of 200 who favor government control on the prices of medicines. (a) Find the mean and standard deviation of the sampling distribution of p. (b) Find the probability that the sample proportion p is at least 72%. (c) Find the probability that the sample proportion p is within 0.05 of the population proportion. (d) Comment on the shape of the sampling distribution of p. Justify your answer. State two properties of the type of distribution you assumed here. Formulae: up = p, op = pa * - - Hx P . - up