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# Please show ALL steps for each part Suppose that, in a certain population, heights of males…

Please show ALL steps for each part

Suppose that, in a certain population, heights of males are normally distributed with mean M1 = 178cm and standard deviation 01 = 4cm while heights of females are normally dis- tributed with M2 = 170cm and 01 = 3cm. Now suppose that a random sample of 25 males and 25 females are selected from the population. a) What is the probability that the average height of the males is greater than 180cm? b) What is the probability that the average height of the females is between 169cm and 171cm? c) What is the probability that the average height of the males is more than 10cm greater than the average height of the females? d) Suppose that we take the average of all 50 heights. What is the probability that this average height is between 172cm and 175cm?

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