Probability & Statistics Ch.2 Section 2 Question 7

· Mohammad-Ali Bandzar

Solutions for “Probability and Statistics: The Science of Uncertainty” (Second Edition). These are solutions I have come up with; I offer no guarantee of accuracy.

Question

Suppose a university is composed of 55% female students and 45% male students. A student is selected to complete a questionnaire. There are 25 questions on the questionnaire administered to a male student and 30 questions on the questionnaire administered to a female student. If X denotes the number of questions answered by a randomly selected student, then compute P(X=x)P(X = x) for every real number x.

Solution

Probability that 25 questions are answered (male student selected):

P(X=25)=P(male)=0.45P(X=25)=P(\text{male})=0.45

Probability that 30 questions are answered (female student selected):

P(X=30)=P(female)=0.55P(X=30)=P(\text{female})=0.55

Otherwise: P(X=x)=0P(X=x)=0 for all x∉{25,30}x\notin\{25,30\}