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Question 2 (4 marks) Part a) A sample of n-25 observations is drawn from a normal population with μ-100 and o-20. Find the following. i) P(X<96) ii) P(96-X-105) Part b) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. i) What is the probability that a professor works for more than 60 hours per weeks? ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours?

Please give the text answer do not with hand writing, Thanks

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Solu tou P x a6 Avea -to the left oa6 スーペ_nUi o.1581 一1.00 (-くas ) P (14-1. oO) t 0.158t (front table) : ρ (y(A6) = 0.158 t 15.84·P (x7 60) din l 51 we conver t ㎡s to stando-d normed US? 60-(51) 6 久- 1.3333 스21.33 P 2 71.33)ra to the Rgh 133 0.0918. -0.90ti) P Y 60) ormot distribution :52, c:8 n: 3 we convert ths -to $ta-dard nor mao usmcr 叹_nU 60-(s) O oiOL (-0.9896

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