1. A student scored 625 on exam A and 45 on exam B. The national average for the

Question

1. A student scored 625 on exam A and 45 on exam B. The national average for these exams are 475 and 30, with standard deviations 100 and 8, respectively. On which exam did the student perform better?

2. An interviewer has time to talk to only two candidates for a job. There are currently three math majors and two Stat majors waiting to be interviewed.

What is the probability the two candidates selected for interview…

•are Stat majors?

•are Math majors?

•have different majors?

What is the probability that at least one candidate selected for interview is a Stat major?

Explanation / Answer

1)

here z score for exam A =(X-mean)/std deviaiton=(625-475)/100=1.5

z score for exam B =(X-mean)/std deviaiton=(45-30)/8=1.875

as z score for exam B is better ; student has done better in exam B

2)

probability the two candidates selected for interview are Stat majors =(2/5)*(1/4)=1/10

probability the two candidates selected for interview are math majors =(3/5)*(2/4)=3/10

probability the two candidates selected for interview are different =P(first math and second stat+first stat and second math)=(2/5)*(3/4)+(3/5)*(2/4)=6/10

probability that at least one candidate selected for interview is a Stat major =1-P(both math)=1-3/10=7/10

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