Question

a) At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 30 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

Find the probability that nine do not use the foil as their main weapon. (Round your answer to four decimal places.)

b) A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 60% of the questions correct. (Round your answer to three decimal places.)

Answer 1

a)

here this is binomial with parameter n=30 and p=P(not using foil as main weapon)=1-0.60=0.4

P(X=9)=

(nCx)px(1−p)(n-x)    =

0.0823

if using ti-84 use command :binompdf(30,0.4,9)

if using excel use command :binomdist(9,30,0.4,false)

b)

here this is binomial with parameter n=10 and p=0.5

probability that the student passes the quiz with a grade of at least 60% of the questions correct (getting 6 or more correct):

P(X>=6)=1-P(X<=5)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.377

if using ti-84 use command :1-binomcdf(10,0.5,5)

if using excel use command :1-binomdist(5,10,0.5,true)