Question 1164785: Please help me to solve this problem.
Q:At a certain large university, the weight of the male students and female students are approximately normally distributed with mean and standard deviation of 180 and 20 and 130,15 respectively. If a male and female are selected at random, what is the probability that the sum of their weights is less than 280?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the means are 180 and 130
the variances are 400 and 225 (square sd)
the new distribution has mean of 310, the sum
and variance 625, the sum of the individual variances, which means the sd for the combined distribution is 25
so probability sum of the weights is less than 280 is
z<(280-310)/25
z< -30/25 or -1.2
probability=0.1151
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