Question

Example 5.27 The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 g and a standard deviation 1.3 g. If 60 batches are independently prepared, what is the (approximate) probability that the sample average amount of impurity X is between 3.5 and 3.8 g? According to the rule of thumb, n = 60 is large enough for the CLT to be applicable. X then has approximately ---Select--- distribution with mean value uy = 4.0 and 3=1.3 (rounded to four decimal places), so 3.5 - 4.0 3.8 - 4.0 P(3.5 < X < 3.8) $ 3.8) PL < 7 < = 323 = $(-1.19) - P( C ) = 0.1156 Now consider randomly selecting 100 batches, and let to represent the total amount of impurity in these batches. Then the mean value and standard deviation of To are 100(4) = 400 and To has approximately a normal distribution. The probability that this total is at most 425 g is the following. PLT, 5 425) z Plzs 425 400) = pz5C ) (rounded to two decimal places) 100(1.3) = 13, respectively, and the CLT implies that 13 (rounded to four decimal places)

Answer 1