In a group consisting of NT =500 marbles, the mean weight and s.d. value of a...

In a group consisting of NT =500 marbles, the mean weight and s.d. value of a marble are 5.02 g and 0.3 g, respectively. 100 marbles are randomly being taken from this group of marbles. Calculate the expected ratios of sample marbles whose total weight a) varies between 4.96-5.00 g, b) is more than 5.10 g

Expert Solution

a)

P(4.96 < Y < 5) = P(4.96 - mean < Y - mean < 5 - mean)
                  = P((4.96 - mean)/(SD/root(N)) < (Y - mean)/(SD/root(N)) < (5 - mean)/(SD/root(N)))
                  = P((4.96 - mean)/(SD/root(N)) < Z < (5 - mean)/(SD/root(N)))
                  = P((4.96 - 5.02)/0.03< Z < (5 - 5.02)/0.03)
                  = P(-2 < Z < -0.667)
                  = P(Z < -0.667) - P(Z <-2)
                  = 0.2296

b)

P(Y > 5.1) = P(Y - mean > 5.1 - mean)
                  = P( (Y - mean)/(SD/root(N)) > (5.1 - mean)/(SD/root(N))
                  = P(Z > (5.1 - mean)/(SD/root(N)))
                  = P(Z > (5.1 - 5.02)/0.03)
                  = P(Z > 2.667)
                  = 1 - P(Z <= 2.667)
                  = 0.004

orchestra answered 2 years ago

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