The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 28 centimeters with a standard deviation of 5 centimeters. Assuming that the sample means can be measured to any degree of accuracy, nd the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters.

Lecture 10/02/2017 → Section 3.2 ← The Multiplicative Rule & Independent Events Probability of the Intersection Multiplicative Rule of Probability: o P ( A ∩ B ) = P(A)P(B|A) o (P(B|A) read as probability of B GIVEN A) Similarly, o P ( A ∩ B ) = P(B)P(A|B) o (P(A|B) read as probability of A GIVEN B) If events A and B are independent, then the probability of the intersection of A and B = the product of the probabilities of A and B. That is, P ( A ∩ B ) = P(A)P(B). The converse is also true, if P ( A ∩ B ) = P(A)P(B) then events A and B are independent. Multiplication Rule for Independent Events: o P ( A ∩ B ) = P(A)P(B)