Question

Can someone help me solving this?

B6. A study is conducted in a class of 360 students investigating the problem of screen cracking in mobile phones. We assume that a) the number of screen cracking events follows a Poisson distributiorn and that b) the expected rate of screen cracking is 1 in 3 per phone per year. i) Write down the formula for the probability mass function of a Poisson random variable withh 3 marks parameter X, stating also the support. ii) What is the mean and variance of this Poisson random variable? 2 marks iii) How many screen cracking events are expected to occur in the observed class of students in 3 marks one semester 1/2 year)? iv) What is the probability (rounded to two digits) of observing exactly 60 screen crackings in the 4 marks] same class over the same period? v) What is the probability of observing fewer than 30 screen crackings in the same class over the same period? Hint first compute the probability of exactly 30 screen crackings, and then 4 marks consider the shape of the Poisson distribution.] vi) What is the probability of observing between 45 and 75 screen crackings in the class in one semester? Hint: approximate the Poisson distribution with a normal distribution.] [4 marks

Answer 1

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