At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
e) Find the probability that six do not use the foil as their main weapon. (Round your answer to four decimal places.)
f) Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon?

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phuongtrantc2002 phuongtrantc2002

06-04-2020
Mathematics

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At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
e) Find the probability that six do not use the foil as their main weapon. (Round your answer to four decimal places.)
f) Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon?

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Аноним Аноним · Answer 1 · 2020-04-06T12:48:45+02:00

We want to perform the "experiment" 25 times, expecting 6 "failures" and 19 "successes", knowing that we have a 0.6 success probability. The binomial distribution states that this happens with probability

[tex]\displaystyle P(X=19)=\binom{25}{19}(0.6)^{19}(0.4)^6=0.0442[/tex]

i.e. a 4% chance.

It would be very surprising if all 25 did not use foil as their main weapon, because we expect about 60% of fencers using it, which is more than half.