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Q The Common Application 1 A Mil MU Account Dashboard Subjects Calendar -9 Inbox History (9 LM 5 support CDmmumth'i U Library c Q A Study skills m Post Anendee Zoom , Please scan probability assignment separately, Scan all the pages in a batch mode, . Assignments must be neatly handwritten in blue or black pen on A4 paper, . Answer all parts below. Marks may be awarded for: Probability_assignment_7_5i X t CourseHero X + save them in a single pdf le and then upload it online in probability module section 0 Correct use of appropriate mathematical techniques 0 Accuracy and validity of any calculations or algebraic manipulations 0 Clear justication or explanation of techniques and rules used c Please show proper working out. Marks will be deducting for not showing step by step working out. . The lifetime of a certain brand of light globe is normally distributed with a mean of 400 hours and standard deviation of 50 hours. (a) Find the probability that a randomly chosen light globe will last more than 375 hours (3 marks) (b) The light globes are sold in a boxes of ten. Find the probability that at least nine of the globes in a randomly selected box will last more than 375 boxes (3 marks) . Let X be a normally distributed random variable with a mean of 6 and variance of 4. Let Z be a random variable with the standard normal distribution (a) Find P(X > 6), (2 marks) (b) Find b such that P(X > 7) : P(Z