Question: Engineering mathematics questions Question 3 (28 marks) Jonny uses his mobile phone for X minutes each day. X is a random variable which may be

Engineering mathematics questions

Question 3 (28 marks) Jonny uses his mobile phone for X minutes each day. X is a random variable which may be modelled by a normal distribution with mean 28 minutes and standard deviation 8 minutes. (a) Find the probability that on a particular day Jonny uses his mobile phone for: (i) less than 30 minutes [7 marks] (ii) between 10 and 20 minutes [7 marks] ( b ) Calculate an interval, symmetrical about 28 minutes, within which X will lie on 80% of days. [7 marks] (c) Find the probability that on 7 randomly selected days the mean time Jonny spends on his mobile phone is at least 30 minutes. [7 marks]

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